electromagnetism - Magnetic field due to a coil of N turns and a solenoid

I have learnt that the formula for calculating the magnetic field at the centre of a current-carrying coil of $N$ turns is:- $$B = \frac {\mu N I}{2r}$$ (where $r=$ radius of the loop, $I=$ current in the coil) And, the magnetic field at the centre of a current-carrying solenoid of $N$ turns is:- $$B = \frac{\mu N I}{L}$$ (where $L$ & $I$ are the length and the current in the solenoid respectively and $\mu=\mu_0\mu_r$ is the magnetic permeability).

As we can see, both these formulas are different. But I can't figure out why that is. (Since from what I have read about solenoids, they are just a number of coils wound closely together).

So my question is- why are there two different formulas for magnetic field at the the centre of a coil of $N$ turns and of a solenoid? (Is a solenoid somehow different from a coil having many turns?)