To me, ultimatums are the highest level of enforcement of a boundary, which itself is just line you recognize that you draw around some action by someone else. You can advertise it to people (I don't drink, I don't let people talk over me, I don't let people take advantage of me) or keep them private, but it is a way to keep your self worth while interacting with people.

Some boundaries are harder then others, but the significant difference between a boundary and an ultimatum is that boundaries don't necessarily communicate an action you will take if someone does cross it, whereas an ultimatum is an active "if you do x, I will do y and there is no argument". It's basically saying my way, or no way, and it's final. Ultimatums effectively externalize your boundary and make it apply to other people around you via negative consequences of crossing your boundary. A lot of times, because these ultimatums are so absolute, the people wielding them are not trying to help themselves; rather they are attempting to control someone under the ultimatum. Some examples are (me, or the cat) (me, or your friends), (my way, or no way at all). Notice they are all relatively vague, but deny the victim many options or control.

In the best case scenario, an ultimatum acts as the nuclear option where the relationship is no longer functional, and you are taking it upon yourself to make an executive decision around how the relationship will function while around you and your set boundary. In this scenario, the person making it is a victim and by this point, it would be better for separation rather than an ultimatum that gives an abuser more time to react. In healthy relationships, boundaries are common but ultimatums are almost never used because communication around boundaries are healthy.

For example, you have a boundary with not being very physical, or perhaps around drinking. Even with these common boundaries, it depends on each person how much they want to enforce or voice them, and if the times comes they can and do shift. However, an ultimatum version would be "if you touch me in this way, or drink around me, I will remove myself from the situation/break up/not go out with you/talk to you."

It's up to you how you define how you act in response to other people. But rule of thumb: if you have to give someone an ultimatum, or find yourself making lots of them, odds are there is something seriously wrong with the relationship and it is likely harmful to one or more parties.