Interestingly, the forms that you liken to "beautiful" actually parse to a native English speaker as "attractive but not quite beautiful".
So, on a scale of 1-10 (10 being the top), "pretty" has the connotation of maybe a 7 or 8 on any scale, beauty or otherwise. And that's basically how it always parses out in English. Just consider it as a 7-8 whatever on a 1-10 scale.
note if the scale is inverse, it's the same. Suppose 1-10 was a scale of ugliness (with 10 being most ugly) "pretty ugly" is still a 7-8 on that scale. Same with "pretty cold" if the 10 means "coldest possible".
"very" is used to emphasize something. "She's very pretty." Means she's somewhere between pretty and outright beautiful, but more on the beautiful side ("she's almost beautiful" has a bad connotation that there's something wrong with her).
"It's very hot" would mean not only is it hot, but it's a little extra hot.
It's like adding a .5 to anything on that 10 point scale.
So if "hot" is 10, very hot is a 10.5.
You rarely use it with words that have a moderate intention, except for specific effect, "it's very lukewarm" is not something you'd probably regularly hear. But "it's very cold" is.
"This curry is pretty hot" would mean it is hot, and hotter than normal, but not very hot in the context of curries.
So there's something in there about the context and that it is a modifier for "more" but not "much more".
>"This curry is pretty hot" would mean it is hot, and hotter than normal, but not very hot in the context of curries. //
Probably what they mean, if they're British - and especially if male, is that the curry is so frigging hot it's bordering on inedible and likely giving them chemical burns but they're going to eat it anyway either to show "good manners" or prove they're well hard.
Personally I often say something was pretty good and mean it as quite high praise or at least better than I expected. I think (hope) my tone of voice would make that apparent though.
Tone of voice and situation sometimes counts though.
In order:
fairly > pretty > [the word] > very