From memory; no, you don’t.
7-zip’s provided executable is /usr/bin/7zz, while p7zip is /usr/bin/7z.
I aliased one to the other on my own system, but otherwise they are compatible.
p7zip should probably stay installed anyway, as it’s a dependency for a number of other packages, serving as compression backend.
That’s the upstream. The 7-zip developer’s website.
To my understanding, p7zip the project started as a fork of the 7-zip project (ie by other people) back in ancient times (ie. I’m too lazy to look up the dates), when 7-zip was windows-only. It made it Linux-compatible. In other words, it was 7-zip for linux.
When upstream 7-zip itself started supporting Linux, p7zip became less relevant and was not always actively developed.
The current “p7zip” package appears to use p7zip-zstd, which is a fork of the old p7zip project; in other words, a fork of a fork of 7-zip.
The “7-zip” AUR package just builds directly on the upstream source from https://www.7-zip.org.
I think that, during the time that p7zip was the only option on Linux, the upstream 7-zip diverged from it in ways that make the two slightly incompatible for the purpose of being used as backend by GUI archivers or other software. By the time upstream 7-zip came to Linux, there was a lot of software that relied on p7zip.
I assume that’s why there is still interest in maintaining a modern version of p7zip — the alternative would be to alter all software that has come to depend on p7zip over the years, to make it compatible with 7-zip.
Disclaimers: This is all from the top of my head, I haven’t followed all this very closely at the time, nor have I done any fact-checking while writing this post. Tracking the phylogeny of open-source projects is not trivial. Anyone with better info, please chime in.