In order to complete Jan's answer destroy adds loading of an object to the memory before deleting it (and calling callbacks). Basically there is a quite a a difference, because using delete avoids callbacks/validations and it might breake referential integrity.
delete
Deletes the row with a primary key matching the id argument, using a SQL DELETE statement, and returns the number of rows deleted. Active Record objects are not instantiated, so the object’s callbacks are not executed, including any :dependent association options.
You can delete multiple rows at once by passing an Array of ids.
Note: Although it is often much faster than the alternative, #destroy, skipping callbacks might bypass business logic in your application that ensures referential integrity or performs other essential jobs.
destroy
Destroy an object (or multiple objects) that has the given id. The object is instantiated first, therefore all callbacks and filters are fired off before the object is deleted. This method is less efficient than ActiveRecord#delete but allows cleanup methods and other actions to be run.
This essentially finds the object (or multiple objects) with the given id, creates a new object from the attributes, and then calls destroy on it.
http://apidock.com/rails/ActiveRecord/Relation/destroy
For further discussion take a look at this post
Difference between Destroy and Delete