A cart popup is a modal shown in response to a shopper action rather than a block that's always present on the page — the distinguishing factor versus cart page or cart drawer isn't capability, it's timing: the offer only appears at the moment it's triggered, which makes this context better suited to a single, specific prompt than to an always-visible recommendation block.
Capability-wise it's identical to the other cart-stage contexts: full behavior-mode range, full styling and layout options.