Yes, partial pressure is what matters. Normal air at 1 bar (1 atmosphere) contains about 0.2 bar of O2. Pure oxygen at sea level is 1 bar of O2.

The article you linked has a graph showing that 0.5 bar of O2 can be tolerated pretty much indefinitely, and it takes hours for significant toxicity to show up at 1 bar. Higher partial pressures cause much faster symptoms.