The "Rebuild Search indexes" will list the system index, used for searches in the Sitecore desktop.
I think the reason that this one is separated from the other is to be found in older Sitecore versions (6..). The system index was the first (and only in the beginning). There was no "Indexing Manager" in those versions. When Sitecore started to use more indexes, the Indexing Manager was introduced and this will now show you all indexes - except the system. Well, actually it is not showing all indexes - some are filtered out (e.g. indexes used for reporting) because they do not want you to rebuild them.
Probably one day the "Rebuild Search indexes" will disappear... (edit: apparently it is gone in 8.2)
Might want to read this old post: https://reasoncodeexample.com/2013/01/22/custom-lucene-net-indexes-in-sitecore/