What does the Soul stone do? Why is it so important? Are the Mind and Soul Stone the same thing?
In Avengers: Infinity War, Thanos has to sacrifice his own daughter to get the Soul Stone when the Soul Stone seems useless.
There is a single moment in Infinity War that demonstrates the power of the Soul Stone. During the battle on Titan, Doctor Strange nearly manages to subdue Thanos by conjuring magical strings (possibly the Crimson Bands of Cyttorak, or a reference to them) and tying all his limbs down with them. In response, Thanos clenches his fist -- and it glows orange (not red like the Reality Stone). Almost all of Doctor Strange's magic is immediately dispelled. Director commentary for the home release confirms this is one of the Soul Stone's powers.
That being said, several of the Infinity Stones have already been used in lots of different ways, some of which could overlap a bit. For example, in Thor: The Dark World, under the right set of circumstances the Reality Stone was able to "merge" several planets together and allow travel between them. This sort of thing might normally fall under the domain of the Space Stone, but... Something, something, mystical syzygy. The Space Stone, meanwhile, was apparently used to charge an engine that wound up giving Captain Marvel a variety of powers, including fast travel through space but also including shooting powerful energy blasts. And the Mind Stone, while generally behaving as you'd expect, also apparently created (or unlocked?) Quicksilver's powers somehow.
Out-of-universe, these things happen in the pursuit of trying to tell a good story. Some things sometimes don't make perfect sense, or things need to happen a certain way in order to set up an interesting plot further down the line or just plain make some fans happy.
In-universe, it seems plausible enough to just say that our Earthly words for the abstract concepts that govern fundamental forces of the whole universe just might not be completely accurate. Perhaps "Mind" is only a rough approximation of what the Mind Stone truly has power over, and perhaps "Soul" is just the simplest known English word available to summarize the domain of the Soul Stone.