All causal synonyms are of the same basic significance. They point us to that which occurs or comes into being as the product of the agency which produces it. Effects are determined by causes. It makes no difference whether the occurrence in question is that of a nail being driven into a board or of a man being influenced to make a choice. The existence of causality is not dependent upon one's awareness or acknowledgement of its presence.
Influences are always fully causal in nature.
An influence that does not influence is not an influence. A cause which effects nothing and affects no one, is not a cause. All genuine influences produce their own effects. They make certain things necessary, even if they do not make other things necessary. The other things have their own causes.