So every single resource online tells me that something like this:
cmp %eax, %ebx
jg < something >
would jump to < something > if eax
When we read something like
cmp $0x2, %eax
jg < something >
we know the assembler used is one that reverses the position of the operands of an instruction. That's because Intel's syntax dictates that the destination operand comes before the source operand and clearly an immediate value like $0x2 can't ever be a destination!
Knowing the order of things we now interpret your first code snippet as
cmp ebx, eax
jg < something > ;jump if EBX > EAX
and the second code snippet as
cmp eax, 2
jg < something > ;jump if EAX > 2
And does this apply to other jump statements as well?
It does.