The suspended-fourth chord type, abbreviated sus4, contains a fourth instead of a third. That is, where a major or minor triad contains a P1 (root), m3 or M3, and P5, the sus4 chord contains a P1, P4, and P5.
This chord is thought to create suspense, in the sense that the fourth is expected to give way to a third. The movement from 4 to 3 "resolves" the suspense.
But you can feel free to use this chord with or without "resolving" the suspension. You can think of sus as meaning substitute. The four note is the substitute for the three.
There is also the less common sus2 chord, which works in the same way. In this case a second takes the place of the third.
You can have a 7sus4 chord. But there's no 7sus2 chord—that's just called a 9 chord. (It's okay if a seventh or ninth chord lacks a third.)
You'll occasionally see a sixth chord, abbreviated 6. It's a major chord with an added major sixth. It functions the same as a major chord, but the extra note makes it "thicker." Note that C6 is essentially the same as Am7/C.
The minor sixth chord is abbreviated m6. It's a minor chord with an added major sixth. (Despite the chord's name, the added sixth is major, not minor.) Cm6 has the same notes as Am7-5/C.
Another note that can be added for thickening is the second, which is also called the ninth. The added-ninth chord, abbreviated add9 (or sometimes add2) is a a major chord with a second added for thickening.
You can add a ninth to a minor chord as well. It's abbreviated m(add9). The half-step interval between the major second (the ninth) and minor third gives this chord an interesting bite.
For maximum thickness, you can add both the sixth and the ninth. The six-nine chord is abbreviated 6/9. This is the one case in rock chord notation where a slash is not followed by the bass note. Note that this chord contains all five notes of the pentatonic scale.
If you add a major ninth to a seventh chord, it's simply called a ninth chord, abbreviated 9. The maj9 chord is a maj7 chord with a major ninth added. The m9 chord is a m7 chord with a major ninth added.
Finally, what if you have a 7 chord and you want to leave out the fifth and play a major sixth instead? This delightfully dissonant dominant chord is usually written as a 13 chord. In theory, the 13 chord should contain all seven notes of the scale, but typically some of the notes are left out.
There are still other possible chord types, and if we were writing jazz you'd want to know every single one of them. But rock is not usually very inventive with chords—many rock songwriters go through an entire career without using any of the chords in this post. So don't sweat over learning all the different chords. Learn them when you need to, when they're useful, and when you're feeling adventurous.