I have a Nikon D5100. My lens is this package 18-55mm AF-S Nikkor lens?

And with these also is Nikkor AF 70-300mm lens. Did I get a good match of lens? I know there's a gap between 55 and 75.Is there anything I missed from this gap? And moreover, what is the difference between AF and AF-S lenses?

You must have AF-s lenses to use the auto focus on your camera. The AF camera will not auto focus. I'd be un-ordering it unless you are very experienced in focusing.
No, you really aren't missing anything in there. It's not a very big gap anyway

The gap between 55 and 70 is not worth worrying about.

AF lenses use the cameras internal focus motor (The nikon D5100 DOES NOT have this), AF-S lenses have their own focus motor inside the lens.

You will have to manually focus with an AF lens. An AF-S lens can autofocus.

As for missing any gap, there are lenses less than 18mm (such as 10-20mm) and more than 300mm (such as 100-400mm) but these lenses cost quite a bit more, and the 18-55mm + 70-300mm is sufficient for a start.

I'd undo the deal too. Manually focusing it is workable, but very inconvenient especially if you are a beginner. Odds are that that lens will end up gathering dust on your shelf.

Also, you shouldn't buy lenses just for the sake of covering focal lengths, but by actual need. There's no point in covering 18-300mm with two lenses if what you really need turns out to be a single 50mm/1.4 prime lens for portraits or a 60mm/2.8 macro lens. That is something you can figure out with the 18-55mm kit lens, when you run into its limitations.

You need the AF-S 70-300mm lens.

If you look at the price difference between the AF and AF-S lens, the D5100 doesn't seem much cheaper than the D7000.

The 18-55 is fine, the 70-300 is probably the old G-type. Doesn't autofocus and is a mediocre lens at best. The "gap" between 55 and 70mm is a big step, nothing more.