It entirely depends on what you want. For me, the command sit (sitz) or down (platz) means don't move until I give you another command. However, both of my dogs also know a stay command (each dog has a different command).
I agree it's a personal choice, both dogs know what the sit or down command entails but there is a seperate "stay" command which is not attached to a certain position which they've learned which essentially means "freeze in whatever position you are in now and don't move until released"
I like the implied sit/stay as long as I don't move. If I get up and move to a different place then I tell them to stay. If I am standing there and say sit or down I expect them to stay in that position until I give a release word or start to move.
The reason I use a stay is dogs usually see a sit down or stand as an action and not a position. Thats why you have to teach a down from a sit a down from a stand and down in motion as separate actions. Doesn't really matter that much though but its the reason behind my preference.
I don't teach a 'stay'. My last command is to be held until I either give another command or I give a release.
I do teach a 'wait'. Meaning, wait before you go through the door or wait inside your kennel after I open the door until I release. I want my dogs to be clear on 'wait', there is no gray area. This command may stop them from crossing the street, or running to meet my husband's pickup (while it's still moving) when he comes home.
Again, this just works best for me. Honestly, there are times when I'll say "Lay down and you better not move!" My dogs get what I'm implying......
I agree with Packen. Sit, down, and stand imply "stay in that position until you get another command or release word."
I do have a "wait" command but this is used by itself not paired with a position. Like say my dog is hiking off leash and gets ahead of me, I say "wait" and he waits until I catch up. Or, if I'm feeding dogs and don't want everyone knocking me around and diving in, I say "wait" and they have to stay where they are until released. I don't care if it's sit, down, or stand, just hold still.
I like to keep the stay command as a separate word so that I can use it coupled with other commands that my dog knows, besides the usual sit/down. I can use it to tell my dog to stay in the back yard when the gate's open (stay here) or keep him out of the house when I'm grabbing a towel to dry him off (stay outside) and even to keep him from yapping (stay quiet) I like using it in that generalized versatile way.