What is the difference between the cmp and test instructions?

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Accepted Answer

cmp sets flags from a subtraction (S1 - S2); test sets flags from a bitwise AND (S1 & S2); neither stores the result — they only update the flags.
Both are "throwaway-result" instructions: they perform an operation purely to set the condition flags, then discard the numeric answer. You follow them with a conditional jump/set/move that reads those flags.

Instruction (AT&T)
Computes
Flags it drives
Typical use

cmp S2, S1
S1 - S2
CF, ZF, SF, OF
Compare two values (<, ==, >)

test S2, S1
S1 & S2
ZF, SF (CF/OF cleared)
Check if zero, or test specific bits

cmpq %rsi, %rdi     # flags from (rdi - rsi)
jg   .L1            # jump if rdi > rsi (signed)

testq %rdi, %rdi    # flags from (rdi & rdi) == rdi itself
jz   .L2            # jump if rdi == 0

Tip: test %rax, %rax is the idiomatic "is this register zero?" check. ANDing a value with itself yields the value, so ZF tells you if it was zero — and it's shorter/faster than cmp $0, %rax.
Go deeper:

CMP — x86 instruction reference — CMP (subtract-and-discard) reference.
 TEST — x86 instruction reference — TEST (bitwise-AND-and-discard) reference.
 FLAGS register (Wikipedia) — the flags both instructions drive.

Instruction (AT&T)	Computes	Flags it drives	Typical use
`cmp S2, S1`	`S1 - S2`	CF, ZF, SF, OF	Compare two values (`<`, `==`, `>`)
`test S2, S1`	`S1 & S2`	ZF, SF (CF/OF cleared)	Check if zero, or test specific bits