I don't think this is fully explained until later in the course, but there is a verb suffix -wI' that turns a verb into a person or thing that does that verb (much like the -er suffix in English). However, when attached to a word that is already a noun, it is, indeed, one of the possessive nouns.
Some of the possessive nouns come in pairs - one ending in j and one ending in '. For those pairs, the one ending in ' indicates that the noun it is attached to is a being capable of language. The one ending in j indicates that the noun it is attached to is not considered a being or not considered to be capable of language. -Daj and -chaj do not come with an alternate and are used with with beings capable of language even though they have a j and not a '.
-wI' as a verb suffix is similar to English -er -- someone who does something or something which does something. (So it's not necessarily a person.)
-wI' as a noun suffix, though, means "my" when the "possession" is someone who is capable of using language.
For example, paqwIj "my book" but jupwI' "my friend". If you said jupwIj, you'd be insulting your friend.
Similarly with -lI' versus -lIj. (So don't talk about SoSlIj to a Klingon.)
(But there is no -Da' -- -Daj is used whether the "possession" can use language or not.)