What is the difference between adapter cards and expansion cards? Can these two terms be used interchangeably?
No, these two terms cannot be used interchangeably.
Expansion cards can only be plugged into a motherboard expansion slot. For example: PCI or PCIe slots.
Adapter cards are any "card adapter" what can plug in to any PC port, to "adapt" the port into another form. The age old saying goes: "anything that adapts a connection from one type/specification to another type/specification".
So that means that all expansion cards that do any type of conversion can be classified as adapter cards.
For example NVMe, because it changes PCIe 4x to SATA spec connection.
Adapter cards can only be classified as an expansion slot, if it is directly plugged in to the motherboards expansion slot.