A buoyancy aid has a foam core, and always provides buoyancy. It's the sort of thing you'd wear while kayaking, but it's far too bulky to want to wear it unless you expect to go in the water.
A life jacket is inflatable, and normally automatic. If you're at risk of falling in, and to do so would be dangerous, you should probably wear one of these -- if you go in the water, it'll inflate automatically. This isn't suitable if you might get wet without wanting the life jacket to inflate, though, and you can get equivalents with manual inflation. The ones you get on aircraft are cheaper than ones you're expected to re-use by wearing multiple times but in neither case will you inflate it multiple times.
The downside of a manually-inflated life-jacket is that you need to be conscious to inflate it. The downside of an automatic life-jacket is that if you get wet, it'll inflate. The downside of the buoyancy aid is that it's always bulky, but on the other hand if you're wearing it, it'll always work.