The biggest mistake I see in screenwriters writing plays, is they "cut to" many many different scenes. So they will have a scene with three lines, then the next scene will take place in an ambulance for four lines, then we will be inside and apartment for three lines etc etc.
Being a playwright, just like being a screenwriter, means you have to understand stagecraft, just as you need to understand film making. You need to know what the limitations are of performing on a stage. You need to understand the differences between audiences for film and theatre. Theatre is a much more aural experience, it's much more about the words spoken than the visuals (and again big generalisations, there are some staggeringly beautiful visually shows out there as well, but I am talking basics here).
Scenes in plays tend to be longer. Often a scene can take up an entire act. Often you will see a play that only uses one set. Remember each set change takes time, you can't just "cut to" anything. You need to get your crew in there to move the furniture while the audience waits. "Effects" are much more complicated on stage. You can't just blow a person's head off for example.
Also you said you were commissioned to write a play, so I assume you also know the sort of space it will be performed in. The space matters a lot for what you can and can't do. You can't hide someone behind a couch if you are doing theatre in the round for example. So: Will it be proscenium arch? Black box? In the round? Traverse? What is the budget for set and costumes? Will actors be playing multiple roles?
This latter point affects the cast of the play. If you want a big cast, then you have to decide if people will be playing more than one part, and make sure that if this is the case, you don't have two parts played by the same person on stage at once. Typically you have much smaller casts in plays for this reason. Remember too that an actor with one line in a play is very different to an actor with one line in a film. In a film the actor comes on set for a day, does his shoot and leaves. In a play this actor has to come to rehearsals, and then every single show, sit around backstage for several hours, before coming on stage to say, "A package just came for you." It's kind of something to keep in mind as well. You can't have "extras" in a play unless you have the big bucks.
I like to explain it like this. Plays are a lot like fourth wall sitcoms a la Friends or Mad About You. In these tv shows you have a clear "audience" and a large set that the actors move around on. They are only seen from one angle. Usually too you have a smallish cast, and maybe one or two guest stars. Now of course it being tv they can have a lot more settings than a play, but if you notice the scenes are usually quite long, and well blocked out.
Films are like . . . films . . . or one of those CSI drama things. Where you have a different scene every two seconds, weird camera work that can suddenly have x ray vision. Here you can have actors playing witnesses who have one line and then are never seen again. Cops who show the detectives to the crime scene, and are never seen again. You can use people to create a sense of time and place and atmosphere. You can use people, as props. There is no audience, it's like we are a fly on the wall in a real life setup.
If this makes sense.
Once you get that difference, then, THEN, you can worry about the format on a page. But to be honest, that is totally the least of your worries. Read some plays. Go see some plays. And then . . . write your play!