How to maintain two sets of separate auto numbered tables?

You're not doing anything wrong, just perhaps missing some of the details. FM autonumbering is a joy to work with once you've got the hang of it, and/but different from most other approaches. (and by "different", I don't just mean flexible and reliable)

Broadly speaking, I'd say you have two options:

1. define two styles for the numbering you use inside tables, let's say TableNumberStart and TableNumberContinue. Define autonumbering so that TableNumberStart uses <n=1> and TableNumberContinue uses <n+1>
   This works because you've made the extra effort yourself.
2. use one style – let's say TableAnchor – to anchor each table, and another style – let's say TableNumber – for the numbering you use inside tables. Define autonumbering so that TableAnchor uses < =0>, and TableNumber uses <n+1>.
   This works because you've asked FM to make the effort for you :-} TableAnchor resets the counter to zero, and TableNumber increments it as required. Note: in the definition < =0> the space before the equals sign is essential. It keeps the counter from displaying on the page.

While you're experimenting, read up on Series labels – so you can manage separate numbering for, say, tables and figures. And on Building blocks – I was so impressed the first time I managed to use numbered heading styles to reset numbering in a list …

HTH