These days we call it "SDR" ram for single data rate. But when it was current it was just called "SDRAM". So yes technically all are synchronous dynamic RAM. But the colloquial terms are SDRAM (or SDR), DDR, DDR2, DDR3.
But if you want to get super technical later DDR standards aren't really synchronous at all. There's a huge analogue component and the input clock is only a reference to feed on board PLLs and calibrate delay lines. It's simply not possible to do a traditional synchronous design at the frequencies involved.
Yes. SDRAM is just synchronous DRAM and I think the last asynchronous DRAM type in widespread usage was probably EDO DRAM from the early 1990's.
The first synchronous DRAM type was called SDRAM and that was followed by all of the DDR standards which still use a clock and are there synchronous in operation.