In connection with most verses in the Tenach Shabat seems to be a term, which is often linked with the seventh day (the day from sundown fridaynight till sundown saturday night; it was evening it was morning; the seventh day), from the roos Shavat which literally means to 'cease', to 'end' (with work) and from these derived 'rest'. It is the day of rest or ceasing with the result in having to stop or rest from work. The Shabat is the day on which HaShem (the seventh) ceased working and “rested.”
Shabatot is the plural form of Shabat.
Shabaton by its ending -on seems to be some kind of Qal pa'al form, while Shabat is a piel form. So one is intensive action while the other denotes a normal action. A rest/ceasing v.s. a complete and total rest/ceasing.
So Shabat Shabaton is a day of rest and ceasing with the meaning of an absolute rest and ceasing from work.