A miniature TCG, also known as "simple TCG", is a TCG without all the fluff. Games are automated, updates with deck releases are sporadic, there is no real option for donations, no member cards, etc; the TCG basically runs itself.
The first mini TCG created was Tiny Legend, a Sailor Moon puzzle TCG created by Rahenna. Tiny Legend was meant to be a sort of extension or sister site to Moonlight Legend.
The idea of a "mini tcg" has evolved slightly over time, with some owners choosing to still update weekly with new deck releases, while keeping the completely-automated games idea.
It is tough to say if these TCGs can technically be classified as "mini" seeing as the average website-based TCG is typically automated and still updated with new cards weekly.