Just being pedantic, but the more accurate term is: secure element. The SE has its own OS (JavaCard) and is usually directly wired to the NFC controller (no iOS in-between).
The iPhone 6 has both a secure enclave, for Touch ID, and a secure element.
"Every time you hand over your credit or debit card to pay, your card number and identity are visible. With Apple Pay, instead of using your actual credit and debit card numbers when you add your card to Passbook, a unique Device Account Number is assigned, encrypted, and securely stored in the Secure Element, a dedicated chip in iPhone."
http://globalplatform.org/mediaguideSE.asp