dejar de vs parar
Both mean 'stop' but dejar de quits a habit or activity for good, parar halts something physically or temporarily.
dejar de
To stop doing something, usually permanently, followed by an infinitive.
Dejé de fumar hace dos años.
I quit smoking two years ago.
A habit given up for good. Always dejar de + infinitive.
Deja de quejarte.
Stop complaining.
Telling someone to quit an ongoing action.
No dejes de llamarme.
Don't stop calling me / make sure you keep calling.
No dejar de = to keep on doing. A negative that means continuity.
parar
To stop movement or an event — a vehicle, a machine, rain, a person walking.
El tren no para en esta estación.
The train doesn't stop at this station.
Physical halt. Parar is the verb of vehicles and machines.
Paramos a comer en un pueblo.
We stopped for lunch in a village.
Pausing a journey. Parar a + infinitive = to stop in order to.
¡Para ya!
Stop it already!
Parar on its own works as 'cut it out'. Parar de + infinitive also exists: 'paró de llover'.
Tricky bit
'Dejé de correr' (I gave up running) vs 'paré de correr' (I stopped running, maybe to catch my breath). Parar can take 'de' too, but dejar de carries the sense of quitting for good.