Meanings of isopropyl, n-butyl, isobutyl, s-butyl and t-butyl and differences between them
(1) Yes, they're alkyl substituents.  But that doesn't mean they have to have been literally added to some other molecule.  There's nothing wrong with speaking about a part of a molecule as a "substituent," even if that exact piece was never actually literally substituted on the main chain in a chemical reaction.  Think of it as a hypothetical substituent.

(2) You get the names this way:

(a) Use the parent hydrocarbon and change "-ane" to "-yl."  So a 4 carbon substituent becomes "butyl" from "butane."  The 3-carbon substituent becomes "propyl" from "propane."

(b) There are two isomers of butane.  The one with 4 carbons in a row is called "n-butane" for "normal" butane.  The other has 3 carbons in a row, with the 4th branching off, this is called "isobutane" from a Greek prefix "iso" meaning "same as," which is the same prefix in "isomer."  Of course it's not the same molecule, but it has the same chemical formula.

(c) There are two ways to attach the group derived from n-butane to a main chain.  You could attach it from one of the end carbons, in which case we call it "n-butyl."  Or you could attach it from one of the inner carbons, in which case we call it "sec-butyl" because the attachment point is a secondary carbon (instead of a primary carbon as it is in n-butyl).

(d) There are also two ways to attach the group derived from isobutane. You can attach it from one of the end carbons, in which case we call it an "isobutyl" group, or you can attach it from the center carbon, in which case it's "t-buty" or "tert-butyl" for "tertiary" butyl because the attachment carbon is a tertiary carbon.

There are only two groups you can derive from propane: the group can either be attached from one of the end carbons, in which case it's a "propyl" group, or it can be attached from the middle carbon, in which case it's an "isopropyl" group.  (There is no isopropane parent, so this is a little inconsistent.)

(3) There are a few names for bigger alkyl substituents, but they aren't as often used I believe, because it starts to get even more complex and idiosyncratic, which is why...

(4) ..these are not the IUPAC names for these alkyl substituents.

You can certainly swear a vow to always use IUPAC names, and many of us have done so when we first learned organic.  But with time comes familiarity with these little guys, who are more compact and roll off the tongue faster than their systematic equivalents, and you should not be surprised if after some years (if you stick with it) you find yourself using them all the time just because it's convenient.