Briefly, no. Acetone and mineral spirits are not the same, and should not be treated as if they are.
Part of the confusion comes from the fact that both are used as thinners . Painters commonly use mineral spirits, for example, to thin the paint that they put into paint sprayers. Acetone, on the other hand, is used to thin lacquer. When people get used to using one as a thinner, they sometimes start using the other for the same application and are disappointed when they do not get the same results.
Similarly, both acetone and mineral spirits are useful for cleaning a variety of messes on tools, in the shop, and around your house. Even here, they are not identical, though. Both are excellent for cleaning up paint spills, for example. While acetone will aggressively strip paint from a wide variety of surfaces, though, mineral spirits is really only effective at cleaning up fresh paint. It can clean brushes and other tools after you finish a project, but once the paint dries, mineral spirits is mostly ineffective.
While the two solvents do have a similarity as thinners and cleaners, ultimately they are different solvents and need to be treated as different solutions to different problems. To get the most out of each solvent, and to make sure that you do not damage important surfaces, tools, or household items, you should learn the differences between mineral spirits and acetone so you use both properly.