Treacle I thought was somewhat in between invert and molasses. Closer to darker invert, but treacle and #4, despite both being black black black, don't taste the same to me (at least not when I've made #4, unless treacle is even darker than #4). I get furious when people say treacle and molasses are the same. The only folks who seem to know better are Brits and bakers.
Every time I've made invert, it's quite thick as well, particularly #3 and #4. As said above, heating it up in hot water before pouring helps thin it out. Same thing you'd do with LME.
The purpose of invert is both flavor and drying the beer out. It's the secret ingredient to almost all real British and Scottish brewing that hasn't really made it across the pond.