Oxygen gain must be oxidized and oxygen loss must be reduced, right

Oxygen gain must be oxidized and oxygen loss must be reduced, right

By all means.
The original concept of redox reaction is that substances get oxygen and lose oxygen
It is found that when a substance gets oxygen, it must lose electrons; When a substance loses oxygen, it must get electrons. Therefore, redox reaction is extended to any reaction with electron gain and loss, which is generally called redox reaction