What is the difference between “secp…” and “sect…”? The National Institute of Standards and Technology (NIST) recommended elliptic curve domain parameters to have names such as “secp…” and “sect…”.

For example: “secp224k1” and “sect571k1”. 

What is the difference between “secp…” and “sect…”?
The sect curves are curves over a binary field. From SEC 2: Recommended Elliptic Curve Domain Parameters (chapter 3):


  The example elliptic curve domain parameters over $\mathbb{F}_{2^m}$ have been given nicknames to enable them to
  be easily identified. The nicknames were chosen as follows. Each name begins with sec to denote
  ‘Standards for Efficient Cryptography’, followed by a $t$ to denote parameters over $\mathbb{F}_{2^m}$ , followed by a
  number denoting the field size $m$, followed by a $k$ to denote parameters associated with a Koblitz curve
  or an $r$ to denote verifiably random parameters, followed by a sequence number.


While the secp curves are over fields over a prime field - or $\mathbb{F}_p$ in mathematical representation. Please read elliptic curve tutorials to understand the difference between the calculations for prime and binary fields.