Do I have to use delta publish to have a delta subscription?

No, that's not required.

Although they are both ways to work with partial updates to messages, delta publish and delta subscribe are completely independent in AMPS. You can enter a delta subscription even if the publishers are sending full messages, and you can publish deltas even if your subscribers are requesting full messages.

One thing to be aware of, though: AMPS needs to be able to parse and assemble the messages you send to be able to provide delta publish or delta subscribe.

AMPS 4.0 supports this with all of the message types provided with AMPS except for the unparsed binary type. If your installation of AMPS uses a custom-developed message type, check with the creator or maintainer of that message type to see if delta messaging is supported.