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.