Q:

Terminology: Tangential Component, Normal Component

Suppose I have a vector field $F$ defined on $\Bbb R^3$, where the input is a path $c:t \rightarrow (x(t),y(t),z(t))$ , a.k.a $F(c(t))$. I am encountering the terms "tangent component", and "vector component" in my studies (without definition) and with a decent amount of Google searches, frankly I am still confused what they mean. 
Is this the correct interpretation:
The tangent component of $F(c(t))$ is $F(c(t))\cdot \frac {c'(t)} {||c'(t)||}$, 
and the normal compoment of $F(c(t))$ is $F(c(t))\cdot \frac {n(t)} {||n(t)||}$,
where $n(t)$ is the normal to $c'(t)$  ? 
Edit: To clarify, here is the references in my textbook in relation to Stokes Theorem.

A:

The confusion comes from two different contexts. For the line integral, you compute the tangential component of $\mathbf F$ — the part of the vector field tangent to the curve. For the surface integral, you compute the component of $\nabla\times\mathbf F$ normal to the surface.

