The way I see it, each one does mean change but the context of the change/degree of change varies for each.
Amend - suggests that, however it was originally, it was wrong. To make something 'right/correct'. In a document, it may be bad grammar or spelling for example.
'Modify' - a change that is more wholesale. Bigger scale change. Making concerted effort to change the make up of something from its original form. Modify settings of a machine. Or code. Or a car is modified (speakers, body) as mentioned above. note there is not right or wrong here.
Revise - re view (look again) something AND make a change based on new information or new opinion. (Note here review is an action where no change is applied).
Hope that helps,