An activated ability that costs mana to activate is not a “mana ability” unless it could also produce mana and has no targets.

Activated abilities contain a colon and appear in the form “[Cost]: [Effect].” Some keywords (such as equip) are activated abilities and will have colons in their reminder texts. Loyalty abilities of planeswalkers are also activated abilities.

Casting Revel in Silence in response to a spell or ability won’t affect that spell or ability. That is, it’s not countermagic.