Synchronous RAM requires an external clock, whereas asynchronous RAM does not. Sync RAM can certainly be faster, but not all designs need sync RAM. Async RAM is generally much easier to design in a system.
SyncBurst (which is a registered trademark of Micron, I believe) is for those sync RAMs where 'n' back to back writes or reads are done for a single command cycle.
In this case, the cycle starts with a command (write or read), and then 'n' (usually 2 or 4) reads or writes are automatically completed. That gives a high burst throughput.
For more details about sync ram in general, see this marketing blurb:
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For specific information, choose one of the datasheets on this page:
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Cheers
PeteS