Not quite right. The gyroscope tracks rotation. It’s really good at telling when your phone is making rapid turns, but has a a really hard time knowing the difference between a stationary phone and one that’s turning very slowly. It also can’t tell which direction it’s starting from.
The accelerometer is used to tell which way is down, by averaging the acceleration of gravity over time. It can get confused while the phone is in motion, but when things slow down it keeps the gyroscope from wandering around.