We can be sure it is the same company through a number of methods:
1.) There is a press release announcing the release of Braiins OS on the SlushPool website.
2.) The OS release is signed by a GPG key found on the SlushPool website.
Thanks for the info @sarcheer. I stand corrected. Here's a link to the press release on SlushPool in case someone wants to review it:
https://slushpool.com/news/introducing-braiins-os-fully-open-source-mining-system/