A mining full node is a full node that not only holds a block chain, accepts other blocks from others according to its protocol rules, accepts broadcast transactions that come along but also constructs a new block from its mem pool on top of it according to his own rules, and broadcasts that new block.
Non-mining full nodes have quite a bit of power if they are operated by exchanges or payment processors. If you can't spend your coins in those contentious blocks they are pretty much useless.