Very basically, Emulsion is just water based.
Acrylic paint uses a water based acrylic medium as its base.
Technically there are more differences and more components to the paint than that but think of acrylic as a synthetic alternative to oil paint, which is how it started.
In our hobby there's nothing stopping you painting with emulsion. A friend of mine produced wonderful ancient Indian and Macedonian armies painted mostly using "matchpots" of household emulsion to give him the colours he wanted. Another friend took advantage of working in the same paint factory as me to use some emulsion and got used the lab to mix up some colours.
Emulsions do (or did) leave a very slight powdery finish and are certainly not so hard curing as acrylics. I'm not sure how they would take a varnish either - there shouldn't be a problem with acrylic over emulsion as there would be a good bind between coats, but emulsion over acrylic could flake very easily.
Latex is a technical term, but iirc it is acrylic household paint, ie an alternative to emulsion.
Now, it's twenty odd years since I worked in that factory and I may be slightly off track, but I hope that helps.