Is a 351 Ford a big block?

No. There were three families of engines for a long time: the Windsor/small-block, the 335/Cleveland, and the 385/big-block. Both the Windsor and Cleveland engines came in a 351 variant (you'll usually see them written as 351W or 351C/M), but neither of these is from the big-block family. Ford big-blocks came in three sizes: 370, 429, and 460.