They are both the same. Soccer is American English for what the British call Football.
There are various types of football (American, Australian etc), but only one Soccer, as far as I know.
Yep. What we Americans call soccer the rest of the world calls football. What we call football is almost exclusively American. (It's somewhat akin to rugby, but that is only a rough comparison.)
Soccer is sometimes used in BE if people are having an informal match in the park, etc. It is very rarely used for the professional sport.
The funny American game is called American Football in BE. ;-)