There is no difference. They are the same thing. They are both defined in config files, and they both are accessible using the Sitecore search API.
It comes down to how the index is used in the system. There are many factors involved: what parts of the system use the index, how long does it take to rebuild the index, how often the index is used, how often the index is rebuilt, is it possible to reliably rebuild the index, etc.
Indexes that appear in the UIs you mentioned have been determined to be safe to display in those UIs.
As for how these indexes are used, it depends on the index. It's beyond the scope of this question to describe each index and what it is used for. You can look in the config files to see what each index is built from. You can use a decompiler to see where Sitecore uses each of them.
Many people are not aware that search indexes provide access to much more than just items in Sitecore databases, or that you can define your own indexes to support your own specific requirements.