I've hosted and been to zillions of pot lucks.
I agree that if it's at my house, I'm the host. Any time I receive people in my home, I'm the host, regardless of whether I provide a glass of water or a full meal or whatever in between.
Most of the potlucks I've hosted & been to are within an organized group that gets together regularly, where the norm within that group is to have a potluck whenever the get together is hosted at someone's house. In that case, the hosts provide the main dish and they let everyone else know what that dish will be in advance so that the rest can plan their dish around that. We do group emails so that as people chime in, everyone else knows that dessert is already being taken care of, for example, and this keeps duplications to a minimum.
Back when my kids were in cub scouts, we used to have an end of year pot luck pool party at a neighborhood pool. In that case, no one was the host and no one really worried about keeping track of what foods were being brought. There were maybe ~30 families and there always just naturally ended up being a good mix of main dishes, side & desserts.
The main difference here being the number of people bringing a dish. If you have a get together with eight couples, you're going to need to organize it so as to avoid too many of the same dish. If you have 30 dishes coming, the distribution will most likely be ok without intervention.
I also have a girls only party once a year that is a pot luck. I've been doing this party for years so most people know the routine but it seems like I'm always inviting someone new who has never been before. My invitation says something like, "Please bring a dish. Let me know what dish you are bringing in advance so that we can avoid duplications. If you don't let me know what dish you are bringing, please don't bring dessert."
Now, I usually have about 18-22 attending this party and almost never have duplications anyway, but back when the party was in its infancy there was one year where I had about 10 girls, and five brought dessert. We did have enough regular food to go around so it wasn't that big of a deal, but all those desserts, well, it was kind of gross. Lesson learned.
As far as how to word the invitation politely, if you call the party a "pot luck" that should be enough to indicate that everyone needs to bring something. Then just say, "Please bring a dish...." along with whatever requirements you have, such as letting you know what they are bringing, or which categories you need, etc. I usually let my girls-party guests know about a week before the party how many are attending but I always remind them that they need not bring enough to feed a full serving for everyone since, with all those dishes, everyone will just be taking a small amount of each.
As a side note, there definitely have been occasions where someone couldn't bring something for various valid reasons. One of the great things I've found about a pot luck is that there is always an overabundance of food so one or two people coming empty handed is not usually a big deal. And as others have noted, as host, I almost never only provide one dish. You just never know who is going to cancel at the last minute or who might bring a tiny amount of food (it happens), etc.
I really love pot lucks. They are a great way to host a group of friends in a casual setting without going to a huge amount of effort. I also have regular dinner parties where I do provide everything but it's nice not to have to and still be able to have friends over. And I love attending them at others' homes as it gives me a chance to make a fun dessert or appetizer that takes a little bit of effort or expense since I'll only be making the one dish.
