Yes, that is the carbon we mean.
There's no real use in using carbon as an everday filter medium; it doesn't remove ammonia, nitrite or nitrate, so there's really not much point having it in there. What it is good for is adsorbing (that's not a typo; aDsorbing is chemically binding substances, as opposed to aBsorbing, which is just sucking stuff up, like a sponge) tannins from bogwood if you don't like the look of 'tea-stained' water (but a lot of fish do like it) or medications; either because you've finished the course, or because you need to change the med you're using.
Carbon will have used up all it's surface area after a few days or a week, and so won't be doing anything useful; it does, however, make quite a good home for bacteria, so only remove one bag at a time, separated by a few weeks, if you want to take it out. You'd be better off replacing it with sponge or ceramic rings or other bio media; then if you do ever have to mediacate, you won't have to lose some of your bacteria before you start treating.