Short Answer: HomeBase Tuneup morphed into HomeBase Maintenance as part of an initiative this past year to move to a modern HomeBase technology.
"HomeBase" is a database of information cached from all the various files you have in 20Data. It is needed in order to efficiently access and display that information (it would take too long to open each file and read all the data in them in order to display what you see or search in the program)
"HomeBase View" is just a window into that database. Depending on what filters, custom views, queries, etc you have active that window of what's shown can change - but the underlying data is still there in the database.
HomeBase Tuneup / HomeBase Maintenance was designed to resync the information cached in the database with the information in your client files. This is needed for example if files are added or deleted from the 20Data folder outside of ProSeries - the Database only knows what it is told, which usually happens when files are open, closed, saved within ProSeries.