When I was read about the elliptic curve cryptography I found some definition about domain parameter of elliptic curve like the follow. But I did not understand something
$p$: prime number. $a, b$: field elements, they specify the equation of the elliptic curve $ E$ over $F_P$,
$y^2 ≡ x^3+a • x+b $
$G$: A base point represented by $G= (xg, yg)$ on $E (F_P)$
$n$: Order of point $G$ , that is $n$ is the smallest positive integer such that $nG = O$.
$h$: cofactor, and is equal to the ratio #E($F_P$)/$n$, where #E($F_P$) is the curve order.
What's diffrence between $n$ & #E($F_P$)? also
I think two are same value. because #E($F_P$) is Curve Order where The number of points on the elliptic curve is called its curve order. and when we do #E * $G$ = $O$.
Is this right or not right?