The difference is what they return when a record is found, or when it’s not found. Consider the following examples:
>> User.create name: 'THE USER' # creates a user with id = 1
>> User.find(1) # returns the user
>> User.find_by_id(1) # returns the user
>> User.where(id: 1).first # returns the user
As you can see, an existing user can be fetched using any of the 3 methods. The big difference with using where is you can chain commands (of course, without calling first first.)
Let’s have a look at when you try to find a record that isn’t existing
>> User.find(2) # raises an exception
>> User.find_by_id(2) # nil
>> User.where(id: 2).first # nil
So here, it’s obvious that when you use find to search for a record that isn’t existing, you get an exception. That exception is ActiveRecord::RecordNotFound which renders a 404 on production environment.
Hope this helps!
UPDATE
Rails 4 uses the following syntax for find_by
>> User.find_by(id: 1) # returns nil if there's no user with an id of 1
>> User.find_by!(id: 1) # raises ActiveRecord::RecordNotFound when no record is found