It's current to see the terms
handler in some API documentations. It is just synonymous or each term correspond to a specific concept?
I used to think that this terms are just synonymous, but I must be wrong ...
These are general terms in programming. Often can mean different things but generally speaking...
Using jQuery AJAX as an example.
Handler, an asynchronous callback subroutine. Handler implements interceptor design pattern. Which is used to handle incoming or outgoing messages and manipulate its values.
A callback is a piece of executable code that is passed as an argument to other code, which is expected to call back (execute) the argument at some convenient time. The invocation may be immediate as in a synchronous callback, or it might happen at later time as in an asynchronous callback.
Triggers are rules, it executes on events.