Ah, good catch there mate! The name Simplified Payment Verification (SPV) can be a bit misleading.

Actually, SPV wallets can indeed be used for making and receiving payments. What "simplified" refers to here is that these wallets don't need the full blockchain to verify transactions. Instead, they only download the block headers and rely on connecting to full nodes for transaction verification.

So they're "simplified" in terms of how much data they need to handle, but still fully capable when it comes to processing payments!