They don't, but you should check with your GM. I find the various DnD gods really don't lend flavor to PC clerics. It seems to be more like, okay, i rolled up a cleric and i pick this domain. Oh and if i have to pick a god, i'll pick XYZ cause it really doesnt matter. Well, that's been my experience anyways. Hopefully it's been different for others.
Ask your GM to flesh out your god a little or do it for him and see if it's cool. Something like, well, i choose to follow Apollo and will pursue his healing aspect which translates to the Life domain. Besides what's in the PHB, i get advantage when i roll for my HP. Additionally, I must:
Choose medicine as a skill.
Donate 20% of my time working at the temple caring for the sick.
Donate 10% of any treasure to the temple.
Must investigate causes of plague and heal those who ask.
Persecute murderers
Thwart those who cause violence.
Slay the undead for they are an abomination
Something like that. That's what i do for the campaign i'm running anyways. The gods have a domain, maybe a couple, along with other criteria. (i tried to do something like a Cults of Prax)