Here’s how to tell if you’re running Cinnamon or Mate.
<pre lang="bash">
inxi -Fxz
Result.
<pre lang="bash">
System: Kernel: 5.4.0-40-generic x86_64
bits: 64
compiler: gcc v: 9.3.0
Desktop: Cinnamon 4.6.6
Distro: Linux Mint 20 Ulyana
base: Ubuntu 20.04 focal
...