Behavior mode is set once per offer but its availability is enforced per context, which is why the same offer can behave differently depending on where it's placed if it spans multiple contexts — though in practice most offers use one context and one mode.
Standard is the default everywhere: accepting the offer adds the offered product to the cart (or, post-purchase, to the order) without touching anything already there. Swap replaces an item already in the cart or order with the offered one — the pattern for "upgrade to the bigger size" — and is only available where the runtime can mutate an existing line item, which excludes thank-you, customer-account, and POS contexts entirely. Auto-add adds the offered product automatically once its Smart Rules pass, with no shopper click required; this is how free-gift-with-purchase offers work, and it's unavailable post-purchase, on the thank-you page, and in customer accounts — contexts where an order has already been placed and can't be silently modified. Mix & match lets a shopper add several of the offered products in one action; it's available almost everywhere except post-purchase and POS. Popup is a product-page-only variant of standard that renders in a modal rather than inline.
The practical rule of thumb: the closer a context is to "order already exists" (post-purchase, thank-you, customer accounts), the fewer modes it supports, because fewer kinds of cart mutation make sense once money has moved. The Surfaces section lists the exact mode support per context.