If an effect refers to a "[subtype] spell" or "[subtype] card," it refers only to a spell or card that has that subtype. For example, March of the Drowned is a card that benefits Pirates and features Pirates in its illustration, but it isn't a Pirate card.

Atzocan Seer's second ability doesn't include the symbol. You can activate that ability even if it's already been tapped, perhaps because you activated its first ability.