Why Shazam when there is already Superman?

Part of what makes superheroes who they are and attracts readers/viewers to them is their origin stories. Superman is an alien with super powers because of his alien status combined with the light of a yellow sun. He's not "one of us", he's an external savior.

One of the central concepts of Shazam is that he could have been anyone. In the film he's Billy, a 14-year-old boy who gets the powers from an old wizard after being chosen:

A boy who is chosen as the "Champion of Eternity" and given powers by an ancient wizard, and transforms into an adult with superpowers when he speaks the sorcerer's name.

This means that anyone could be Billy. Anyone has the chance to become the "Champion of Eternity". It's not decided by something inborn like what your species is, but by the person inside. While you can't ever be Superman because you're human, you could be Shazam. This gives a slightly different appeal/audience to the character.

On top of that, the fact of him really being a teenager gives filmmakers more time to have fun with the character, which is evident in the trailer. You get a comedic superhero film instead of a serious one - I think we can all agree that the recent Superman films are a bit... grey.

So, that's the main answer for me. Different origin story and different tone make a different character even if the powers are somewhat similar...

For reference, Shazam's full slate of powers are somewhat broader and slightly different than Superman's:

These powers include: the wisdom of Solomon, granting increased intellect; the superhuman strength of Hercules, the superhuman stamina of Atlas; powers from Zeus, including the ability to summon lightning as well as being nearly indestructible; the increased courage of Achilles; and the superhuman speed of Mercury, which provides him with the means of flight.

For example, control of lightning isn't really quite the same as shooting lasers out of your eyes.

As to whether it's part of the same DC universe, one of the longer previews (second in the "trailer" link above) shows icons of Batman and headlines in newspapers about Superman (1:34 in timecode) but the film is set in Philadelphia (according to the Wikipedia article) and Billy's foster brother is referred to knowing things about "this caped crusader stuff". The "Certificate of Authenticity" in the image below from the preview may indicate that everything in the drawer is an artefact from a superhero film/TV show rather than being from the world they live in.

This can be explained by watching The Big Picture - CAPTAINS COURAGEOUS

Shazam was originally called Captain Marvel and was created by Fawcett after Superman because, as Movie Bob explains, almost everyone was trying to make their own Superman after his success. However National Allied Production, who created Superman and felt they invented the genre, began to sue everyone including Fawcett for ripping them off and ultimately Fawcett lost however since the "Golden Age of Comics" ended, no one cared.

When the Silver Age came DC Comics, which was National's successor, bought the rights to Shazam from what was left of Fawcett. however they wanted to release it under Captain Marvel but before they could, Marvel registered the Trademark with Captain Marvel.

So DC didn't go and invent a new Superman, they bought the rights to a character and its IP from another who, at the time it was being released, was more popular than Superman.

as for any connection to the DC Universe in terms of movies/TV we don't entirely know. i don't recall seeing Shazam's lighting crest in Batman V Superman and i haven't heard of any mention to him in the Arrowverse. at this point in time i would just assume stand alone movie

The biggest difference appears to be the character themselves. Yes, they have very similar powers, but good superhero films don't tend to focus solely on displays of those powers, they get old very quickly and there is not much you can do with them.

Motivations and alignment influence a character and the stories quite a lot, as well as their antagonists which they can play off of.
Superman is best described as Lawful Good, and that limits his stories to ones where he generally just upholds justice as he sees fit. Shazam, at least the movie incarnation, appears to be more of a morally grey character as he is still effectively a child. The types of stories you can tell with the two of them are vastly different, even though their skill set is effectively near identical.
Being a child means that Shazam is more malleable as a character, and the writers could in future lead him down different paths that aren't really consistent with Superman. Plots such as corrupting power don't particularly mesh with Superman since he has had his powers for an established period of time, but it would be an organic evolution of Shazam if the writers took him in that direction since he is still immature and given more power than he can really handle.

As noted in other answers, going back in comic book history, the character now being called "Shazam" was known as Captain Marvel. He pre-dated the Captain Marvel who you now see on the screen and who originated with Marvel Comics. This earlier Captain Marvel was a competitor (in terms of comic book sales) with Superman and was actually more successful for a while than Superman. That led to a lawsuit which eventually led to shutting down the Shazam Captain Marvel (and ultimately allowed Marvel Comics to create another character with the same name). Eventually DC Comics (owners of Superman) ended up owning the Shazam Captain Marvel. Back in the 1970's there was a kid's Saturday morning TV show based on the character and DC actually published some new comics featuring him.

Skipping forward to today: Generally speaking, Marvel Comics has great success bringing their characters to the big screen. While there have been notable exceptions, DC Comics has not been as successful. Some of that is seen as the sorts of characters DC has brought to the screen - some people say Superman is too stiff and even too powerful. Going back into the archives and bringing the Shazam character to the movie screen allows for a departure from the straight-laced Superman/Clark Kent character while continuing to allow an extremely powerful hero to be featured. Having the character be a teenager finding his way in the world and learning to use his powers allows more opportunity for moral ambiguity and comic relief.

Also, it's possible that Superman is a bit overused, while Shazam hasn't really been seen in 40 years or more, and so will seem fresher to audiences who don't know him. At the same time, it may feed on nostalgia for those of us who remember watching him on TV as youngsters.

Now, if they'd just bring back Isis ...

It's pretty common to actually have multiple heroes and/or villains with the same powers or abilities in the same universe. This allows to present the same abilities from the view of a different character. We have Superman/Power Girl/Shazam/Wonder Woman/Martian Manhunter (to name a few) who all arguably have the same power sets, these character archetypes are known as flying bricks, which allow for more exotic conflict -- world ending situations that require that level of super hero ability. That said, the way Superman might deal with a world ending entity (trying to reason with it) varies differently than how Wonder Woman (killing it with great intensity) or other heroes would deal with the problem.

Along the same vein, a common dichotomy in comic books is Bruce Wayne as opposed to Dick Grayson. Effectively both men are capable filling the bat-shoes (and have), but while Bruce brings a singular mission Dick does not, he's more of an emotionally driven super hero, albeit having the same abilities (including bank account) as Batman. A third bat-like hero is the current Robin, Damien Wayne, who while having the bat abilities has none of the hang ups on killing people as Bruce Wayne or Dick Grayson. These personality and methodology differences help drive the narrative and conflict further than "Caped Crusader beats up bad guy". As the CW has also shown us, Green Arrow can also approximate Batman's power set.

Other groups of heroes with the same powers (The Green Lantern Corps) also exist -- the Lanterns all have the exact same powers, it's the character interactions and motivational differences that create the narrative here, not "Intergalactic hard light space army smashes space monster with green light blocks".