They are not, although Poolside FM was the first one to use the "Poolside" name.
Poolside AI filed a trademark infringement against "Poolside FM" that forced Poolside FM to change their name to "Poolsuite"
https://x.com/Poolsuite/status/1398007075435843592
This annoyed the founder of Poolsuite and they ripped off his brand.
Poolside AI was only founded in 2023. Poolsuite changed their name in 2021 because of a trademark infringement with the band Poolside, from LA.