I would say that they are synonyms, but not in all cases. So I'd distinguish several meanings of try:
- Taste, sample, or otherwise test in order to determine strength, effect, worth, or desirability.
In that meaning the only possibility is "Probar".
E.g. I have never tried the Spanish omelette.
Nunca he probado la tortilla de patata.
E.g. You can try the car to check it's worth it.
Puedes probar el coche para comprobar que merece la pena.
- To make an effort; strive; endeavor.
In this case it would be translated as "intentar", "tratar de", "procurar"; but not as "probar a".
E.g. They tried to win the match but they couldn't.
Intentaron ganar el partido pero no pudieron.
Trataron de ganar el partido pero no pudieron.
Procuraron ganar el partido pero no pudieron.
It can be translated as "intentar", "tratar de" or "probar a".
E.g. As he couldn't open the front door he tried to open the back door.
Como no podía abrir la puerta delantera intentó abrir la puerta trasera.
Como no podía abrir la puerta delantera trató de abrir la puerta trasera.
Como no podía abrir la puerta delantera probó a abrir la puerta trasera.
Tratar deis most common, except for tasting something;probarmust be used. – Cayetano Gonçalves Feb 13 '12 at 5:00