The Rambam is referring to both points.
You can acquire a slave- i.e. someone who is already a slave- by purchasing them etc.
Or can you can acquire a slave- i.e. a free non-jew who is becoming a slave- by purchasing them etc.
The term "acquiring" refers to both aspects.
FWIW, I heard from a dayan that this is still relevant nowadays.
There's a big problem of how mamzerim can become married practically.
Besides the prohibition against marrying a "regular" jew, even with those jews with whom a mamzer may marry (another mamzer, a convert tc.) the children will still remain mamzerim.
The solution to "purify" mamzerim- let them marry a shifcha canaanis (female slave) which is permissible for a mamzer. The children born are considered avadim, (non-Jewish) slaves, not mamzerim. Then the father can convert his children, and they are regular converted jews- not mamzerim.
The dayan told me that contemporary poskim will use this leniency even today.
They will approach a non-Jewish woman who wishes to convert and offer her to become a shifcha instead, for the purpose of marrying a mamzer to "purify" his lineage.
(A shifcha has the same halachic responsibilities as a Jewish woman would anyway.)
Then, any children born are converted. After the woman is beyond child-bearing age, she converts at that point.
The whole thing is kept a secret; no one realizes that the "convert" was actually a non-Jewish shifcha the whole time!
The dayan mentioned that there's a machlokes between gedolim (he mentioned Rav Aharon Kotler, Rav Moshe Feinstein, the Satmar Rav and "others") about how to create the "shifcha" status.
The issue is- since nowadays in Western society slavery is outlawed, there is no way to actually "buy" a slave since the sale would be void.
According to some poskim the couple would need to travel to a country which actually allows slavery (like many African or S.E. Asian countries) and live there.
Others held it was enough for the marriage to take place in that foreign country, and then afterwards return to the US (or other western country without slavery). (Even though the sale becomes void when they return to the US, once the sale was valid the woman became a "slave." Even though the US will negate his ownership of her, she still remains halachically a slave.)
Apparently today, it's done by entering the Embassy of such a country. Since it's under foreign jurisdiction that's considered enough.
All this I heard from a dayan in a talk. I unfortunately was unable to ask him for sources, though he mentioned that the poskim discuss it in their teshuvos.