Is a memory stick the same as a flash drive?

Answer 1

Usually yes, however Sony does have a product called a "Memory Stick" which ISN'T a flash drive but instead a some what proprietary memory card standard that you can use in Sony cameras, PSP, and PS2 / PS3

Check whether or not the device lists "USB" as the interface or plug. A Sony Memory Stick card would not list USB as the way it connects since it's a card not a flash drive. As long as the description of the item actually says it uses USB, then you are OK. Otherwise don't take a chance.

Flash Drives are also sometimes called:
USB drive, Thumb drives, portable drives, removable drives, pocket drives

Answer 2

Yes indeed...

you could call it a
memory key
USB key (or in French clé USB)
flash drive
memory stick
USB stick

Memory Stick and USB stick being the most common and Universally accepted.