Pretty much. Those machines are typically referred to as oxygen concentrators, which is a solid description of what they do. Depending on brand and settings you're getting somewhere between 50-95% O2 in contrast to sea level ambient air which has about 20% O2.
Even the bottled stuff isn't "pure oxygen" but rather high concentrated oxygen, around 95%. Its made with the same technology you have at home just with an industrial size machine, pressurized into bottles and shipped. For the most part pure oxygen has few uses outside industrial applications.
"Pure oxygen" is unnecessary for treatment of respiratory problems. Your lungs absorb nitrogen as well as oxygen, so with an oxygen treatment the O2 is increased and Nitrogen decreased to correlate to the loss of respiratory function, and your body gets the O2 it needs.