The word **than** is used in comparative constructions. Its complement, in your sentence **mine**, is one of the comparands.

> Our car is older than their car.
> 
> Our car is older than theirs.


With **different** you will encounter **from** and **than**, and also **to** [now and then][1].


> Our car is different from|than|to theirs. Ours is AWD with a CVT and theirs is
> a standard transmission with front-wheel drive, but otherwise they look identical.


  [1]: https://books.google.com/ngrams/graph?content=different%20to%2Cdifferent%20than%2C%20different%20from&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cdifferent%20to%3B%2Cc0%3B.t1%3B%2Cdifferent%20than%3B%2Cc0%3B.t1%3B%2Cdifferent%20from%3B%2Cc0