The difference between cmpl and cmp

According to my understanding cmpl compares unsigned.

It does both, in a way.

The difference in signed vs. unsigned is here the usage of the jump instructions.

For >, there is ja for unsigned and jg for signed (jump if above and jump if greater).

For <, there is jb for unsigned and jl for signed (jump if below and jump if less).

To be exact, here is the meaning of several jump commands:

For unsigned comparisons:

JB/JNAE (CF = 1)           : Jump if below/not above or equal
JAE/JNB (CF = 0)           : Jump if above or equal/not below
JBE/JNA (CF = 1 or ZF = 1) : Jump if below or equal/not above
JA/JNBE (CF = 0 and ZF = 0): Jump if above/not below or equal

For signed comparisons:

JL/JNGE (SF <> OF)          : Jump if less/not greater or equal
JGE/JNL (SF = OF)           : Jump if greater or equal/not less
JLE/JNG (ZF = 1 or SF <> OF): Jump if less or equal/not greater
JG/JNLE (ZF = 0 and SF = OF): Jump if greater/not less or equal