If you're familiar with WordPress, you can categorize posts globally using Global Edit.
However, if you are trying to show recent posts and your slider is set for let's say 5 posts, you only have to recategorize the last 5 posts. If that's too much work, then I apologize. I had no idea how many posts the slider should display, but I don't think it's a good idea to display more than 10 as it will be a massive memory drain on your server and slow it down when loading. I limit my site to 8 for proper memory management.
To answer the second part of your question, a post may be in multiple categories at one time. So, if the slider is only picking up "latest" as its source, if the post is in Cars and Latest, it will display on the basis of Latest, not Cars. If the post isn't in the "latest" category, and only Cars, it will not appear in the slider.