What traits do theater actors have?

Well, from my personal experience - having acted and crewed in both film and theater - there's a certain expectance that theater actors will "play to the back." In other words, they will likely speak louder than natural, enunciate more, and will often use slightly bigger gestures so that what they're saying and doing translates better for the audience sitting in the back of the theater. (Whereas in film - TV, movies, etc. - the cameras and microphones will likely be able to pick up smaller gestures and softer voices, and what little "playing to the back" is actually still necessary - usually in the context of movie theaters - is left to editors, sound designers, etc.) You may notice certain habits of stage-turned-screen actors in early films, especially. A lot of early talkies often feel slightly stilted and exaggerated precisely because nearly all the actors are used to playing it up a bit either for stage or for silent film. (I find L'Atalante to be a good example of this - an absolutely beautiful film, but you can tell at many points that the actors and filmmakers come at it from a very theatrical perspective.) It works the opposite way, as well, obviously - an actor who isn't used to using his diaphragm will hardly be heard if he goes onstage without doing some serious work on his vocal projection skills.

Similarly, a lot of theater actors are used to moving and talking to each other in ways that would likely feel very unnatural to somebody not used to being onstage - namely in the way that they "cheat out" so that the audience can see their faces better/don't have to stare at the actors' backs while straining to hear what they're saying. Depending on how surrounded the stage is by its audience (as some theaters only put the audience directly in front of the stage, while other stages will be surrounded on three - even all four - sides), "cheating out" may take some very strange forms - I have quite a few memories of standing in corners and walking figure-eights across a stage so that no one section of the audience would be stuck staring at our backs for too long. That said, this is more likely to be an issue for film actors trying to transition into theater than the other way around. Cheating out is a thing that sometimes happens in film, as well, but not nearly as often, seeing as cameras make it easier to capture actors' faces and voices even as they stand in a more natural position to talk with each other. (Indeed, if there's any explicit advantage that a theater background can give you when you're looking to transition to film, it's that you'll be pretty used to putting yourself in weird/unnatural positions for the benefit of the audience.) Of course, film/TV actors have their own sets of challenges in terms of putting themselves in unnatural positions for the sake of the audience (and, in this case, the camera).

The most prominent thing that comes to my mind (probably because I'm short and have had to take advantage of these on multiple occasions - even just as a member of the crew): apple boxes. While occasionally used for sound mixers/boom operators who are too short for their own good (read: me), these fellas are generally used to lessen the height difference between two actors who need to appear in a shot together. And believe me, it's an art, making a scene/performance feel natural when you're using apple boxes on and off.

But one of the things that's most noticeable is that, unless the actor(s) and director(s) make a conscious stylistic choice, screen actors are generally expected to not look directly at the camera (and instead look a little above/below or to the side of the camera - whatever works best for the eyeline), since it will otherwise feel kinda unnatural. (You can generally tell when an actor looks into the camera on purpose, and when she does it because she just isn't used to acting for the camera.) A good example of an actor looking straight into the camera (and how awkward/weird/silly it can get) would be the rather silly scene from The Return of Captain Invincible, in which the evil Mr. Midnight (Christopher Lee) sings to Captain Invincible (Alan Arkin) to "Name Your Poison" (even then - in a scene where you can tell that he was directed to break the fourth wall - Lee doesn't always look straight into the camera, and you can tell just how unused to direct camera-gazing he is):

And then there's the challenge - especially in today's sci-fi and fantasy films - that many actors face of acting across from somebody/something who either isn't actually there, or who looks very different from how they will actually look once the editors and CGI artists are done with the film. One of the easiest examples to recall is Andy Serkis's Gollum in the Lord of the Rings and Hobbit movies, though there have certainly been more extreme examples where actors are playing against tennis balls and the like:

Even on a more basic level, many actors have to get used to filming certain elements of a scene with a reader, rather than the actual other actor(s) in a scene, due to differing availability/schedules and other logistics. (e.g. I've been on sets where we called it a wrap for one actor because all we had left was close-ups for the other actor, so in the end it was easier to just deal with the one actor who we actually needed to show on-camera.) One of the most famous examples of this "acting to nobody" (or acting to a random reader/crew member) scenario is Humphrey Bogart's iconic nod of approval for the singing of the Marseillaise in Casablanca:

He filmed that one nod separately from the rest of the scene and was, in fact, nodding to nobody (didn't even know who he was nodding at or why, as the story goes). In scenarios like these, the actor gives a lot of trust to the director, cinematographers, and editors that they will string the story together so that whatever the actor does works and makes sense with the rest of the scene. (And any flubs you may notice in those scenarios are, often as not, as much a result of sloppy editing and/or direction as it is a result of how the actor reacted to the situation.)

You're right that the methods of performance (film/TV/stage) do tend to affect the way an actor prepares for her performance and how the crew treats her. Personally, my general experience is that theater will often involve a lot more prep time for the actors specifically - rehearsals, etc. - precisely because they have to memorize everything they need for the whole show, so they can go through it every night without having to stop in the middle and call for their line. (Though rumor has it that back in Shakespeare's day, they had readers on hand for actual performances, precisely because forgotten lines were so commonplace.)

On the other hand, for film projects that I've worked on, we've often done the table reading and then just had an hour or two of rehearsal for each scene (sometimes less), settled on blocking and whatnot, and essentially said, "Okay, have this scene memorized by Friday, when we film it!" This often leaves a lot more interpretation up to the actor, though of course it depends a lot on the director and his/her style.

In terms of punctuality, I've found that it really depends more on the individual people and the community where you're working, rather than generally on film vs. theater. I've been involved with theater troupes where everybody will get to the theater a half-hour early; and I've directed shows where five minutes late to rehearsal is the norm. Alternatively, I've worked with film actors who are constantly punctual, and with film actors who are regularly 30 minutes late to everything. Of course, this is just my personal experience with punctuality.

In any case, I hope this answered your question and I didn't get too tangent-y!