Exact vs. conservative I'm having trouble understanding definitions.

What's the difference between something being exact and being conservative? I understand both involve proving that a potential function $f$ exists such that
$$\vec{F}(x,y,z)=M\hat{i}+N\hat{j}+P\hat{k}=\frac{∂f}{∂x}\hat{i}+\frac{∂f}{∂y}\hat{j}+\frac{∂f}{∂z}\hat{k}$$
but I'm not understanding what makes something exact as opposed to conservative, or vice versa.

Is it just that differential equations can be exact and vector fields can be conservative, or is there more to it?

EDIT: Fixed a mistake.
Exactness is a property of differential forms, like $M \,\mathrm{d}x + N \,\mathrm{d}y + P \,\mathrm{d}z$. In particular, if a differential form $\alpha$ is exact, then the equation $\alpha= 0$ is also said to be exact.
Conservativeness is a property of vector fields, like $(M,N,P)$.
They are particular case and general case:

Differential forms are a generalization of scalar/vector fields.

Exterior derivative is a generalization of gradient/divergence/curl.

${\bf F} = \nabla f$ is a particular case of $\lambda =d\omega$.