I think youre blending lots of different terms together.
The round nose, the hollow point, the partition, the boat tail, the spire point are all "soft point" bullets. They have the soft inner lead exposed which allows for quicker expansion. In this pic none of them are solids, they are all lead cores with copper jacket however the FMJ doesnt expand similar to how a solid doesnt expand as much.
View attachment 7128821
Solids can have the same sort of design features, they just do so without the lead core, usually its entirely copper or brass (Ill get to solid lead later). Typically people like solids for extreme long range as you dont have lead inside the bullet that can get disturbed or uneven. They are a solid piece of metal so there shouldnt be any discrepancies in bullets internal balance and so on from differing materials. Its easier to machine something out of a completely perfect solid material than it is to try and make a completely perfect bullet by mechanically casing one material inside another.
So typically the solids dont expand as much... unless they are designed to expand.
Here is a solid bullet... only it has the open hollow point style tip to expand easily.
View attachment 7128826
So really your choice is not between two things but two choices between four things.
Conventional lead core copper jacket bullets can both expand (the soft point, hollow point, partition, spire point etc) or they can not expand (FMJ).
Solids can both expand (makers, lehigh) or not expand (warner flatlines).
So
solid target bullet
solid hunting bullet
copper-lead target bullet
copper-lead hunting bullet
So thats the normal bullets, if you want to get into just solid lead bullets only then thats a whole other pack of worms. But similar to the solid brass or copper bullets they can also have expanding vs non expanding designs. Lead bulets are usually shorter and squatter than the copper/brass solids and cant be controlled as perfectly as the copper.brass so they arent as good for long range. A bit more old school.
Design intent has just as much of an influence in the bullets behavior as materials or manufacturing process.