I think that when Zeke says he'll give Reiner's armor to someone else, he means Reiner has a younger relative that could obtain it. The flask's label from which Eren got the hardening ability implyed Braun was a bloodline like the Reiss. And also Eren didn't get a full armor.
It’s possible Zeke was speaking metaphorically. He may have simply been suggesting he was going to pull Reiner from the job and replace him with someone else. It’s also possible he’s threatening Reiner with death. The whole exchange was chilling.
The serum Eren ingested was clearly labelled “ Armor Braun”, making a strong possibility that Reiner’s bloodline is connected to the armored serum. But if I’m thinking through all available options, it’s possible the RBA are not using their real names. “Braun” may also be Reiner’s alias.
I agree that “armor” and “hardening” abilities are not the same thing. The vial Eren ate was called “armor”, but it seems more in line with what the Wall Titan can do. Reiner’s armor seems to be another thing entirely. I think it helps clarify our understanding of getting an ability as a base type vs as a power up.
Reiner is an “armored type” titan. Eren is a “normal type” titan with an armor power up. Likewise, the Wall Titans are “colossal type” titans with an armor power up. I can’t be adamant about this, but it seems to make sense.