To put it simply, a motive is a specific cause for one's actions, while motivation is the driving desire to do something.
For example: An individual's direct motive to become a better person might be because they had made terrible mistakes in the past. An individual's motivation to become a better person may come from a desire to make the world a better place.
While it is true that motive tends to have a negative connotation and motivation tends to have a positive connotation, this is irrelevant to the grammatically correct usage of the terms "motive" and "motivation".
Keep in mind that motive is more specific than motivation, which is a more general term.