Bitcoin Performance: What does Hashes/Second Mean?
SHA256 uses a compression function that maps a 64 byte input block and a 32 byte chaining state to the next chaining state. It divides the message into 64 byte blocks and hashes those sequentially.

The bitcoin proof of work uses SHA256(SHA256(block_header)). Between each hashing attempt only 4 bytes in the last block of the header change, so for each hashing attempt you only need to compress that last block of the message and then one compression for the outer hash.

So one bitcoin hash corresponds to two SHA-256 compressions. In definition of "Hash/s" says how many nonces can be evaluated per second which is a meaningful definition in this context.

The header contains the (root of a tree)hash of the actual block. But since the actual block only changes every 4 billion nonces, the cost up updating it is small compared to the cost of hashing the header. That's why it's neglected in those performance claims.

To compare different hardware you need to use miners specialized for that hardware. There are CPU, GPU, FPGA and ASIC based miners. Mining hardware comparison on the bitcoin wiki lists the performance of many different kinds of hardware. Nowadays only ASIC is competitive, for other kinds of hardware the cost of buying and electricity exceeds the earned bitcoins.