Hi Olga:
Here are the meanings in the dictionary and examples:
Empezar _________
· To begin, make a beginning to something (la próxima semana empezaremos los seminarios)
· Start the use or consumption of something (¿has empezado otra botella?)
· Start something (el partido empezó a las cinco)
Comenzar _________
· Start a thing, start (la función ha comenzado).
Of this you can deduce that they are synonymous, although there can sometimes be some nuance. Maybe "comenzar" is a little more formal.
Hope this helps, Olga. All the best!