An action cad is something that can be done to a token. It can be a blockchain transaction (transfer-ownership) or integration (start-engine, for a car token). They are contextual, meaning some actions is available in some context. For example, "lend" action is available for the car token owner, but not for the person who borrowed the car token to use, since he can't further lend it to another.
When a user starts an action, the action card is drawn. The user could do some interaction like filling a form on that action card, then confirm the action. Upon confirming, an action sheet is sometimes used to preview the result of the action. The word action sheet is borrowed from iOS.
I've made some rudimentary drawing to illustrate the difference.
First, an action card - in this case, transfer DAI to xDAI:
Then, an action sheet opens to preview the effect of the transaction:
The action sheet is coloured with a pattern. The content of the action sheet is cluttered - we need to fix that - but the concept is clear.