Yes, they make their own oxygen.

Here is the "stationary" one I own. Note, it has wheels:
https://www.1stclassmed.com/respironics-everfloq-1
Here is the portable:
https://www.1stclassmed.com/inogen-one-g4-portable-oxygen-concentrator
I chose the Inogen One G4 because it was lighter weight than most. But as Jake points out, the number of liters it puts out is important, I need three liters, so the G4 will take me to the next level as my breathing deteriorates.

It has been several years since I purchased the portable so I believe the following is accurate but may remember incorrectly: Another consideration is if it is "pulse" or steady flow. Pulse produces oxygen when a person inhales. Steady is a constant flow of oxygen. The "steady" uses up the battery faster.

There are many brands. I was most attracted to Inogen and Philips. Inogen is well known, in part, because of advertising. And there are many suppliers. I looked locally but they were far more expensive than on-line. (Because of so many options among portable concentrators and suppliers, I made a spread sheet. But that is me. I think, after all, that I purchased the one that most interested me at the beginning. I could have saved myself a LOT of work.)

Sonnig