Without hanging up on the definitions; Combo is a set of items that work extremely well together, specifically. Synergy is a set of items that work well together in general. Zombies are synergistic. Forbidden Fruit + Transfusion is a combo. (In the situation Transfusion is only around to facilitate a Fruit kill)
I agree with merccer here: Combo is a specific combination of things that achieve something: Slam + poisonous fumes is a combo, blink + relic is a combo, Strip armor + shockwave is a combo. Synergy are groups of thing that work well together but in a more general way, like global buffs are better the more champions you have out, damage bonus are better given long range/multiattack champions, fire charge is synergetic with many weak fire sources and not synergetic with stronger but fewer attacks, relocating/hasting is synergetic with slow units.
Agree with Mercer. Also I think Synergy is often intended by developers, while custom combos are more related to players creativity and harder to discover.
Got the perfect example: Tortuns are (supposedly) high damage champions with ponderous so they are synergetic with quickening and quicken, but tortalleon pygmy + quicken is beyond this simple synergy, it's a combo.