The are five types of adapters you can create in OIM.
1)Process task adapter:- Which is used with process task.Which you will create with process definition. (e.g For Create User)
2)Task assignment adapter:- Which is used to assign of a process task to a user or group.
3)Rule generator:- which is basically used with Form's field.
4)Pre-populate adapter:- Which is basically rule generator adapter which can added
to a user-created form field. Which basically populate user field with using adapter but do not save that data into OIM database.
5)Entity adapter:- which is basically created for form field.This adapter will executes on criteria like pre-insert,pre-update, pre-delete, post-insert, post-update, or post-delete. When any of this criteria fullfilled then this adapter will be called and will perform operation on perticular field and saves data into OIM database.
(Note:If you looking for how to configure connector in design console then please click here)

When you create adapter tasks, You have to provide you jar file which contains java classes. For this you need to use <Xellerate_Home>/Xellerate\JavaTasks folder.

Lets now in little bit more detail about each adapter.
WIll update later....