Local Minima :- $f(x)$ will have local minima at $x=a$ iff $ f(a-h)>f(a)<f(a+h) $where $h->0$
Local Maxima :- $f(x)$ will have local maxima at $x=a$ iff $f(a-h)<f(a)>f(a+h)$ where $h->0$
Global Minima :- $f(x)$ will have global minima at $x=a$ iff $f(x)≥f(a)$ ∀$x$∈ Domain of function.
Global Maxima :-$f(x)$ will have global maxima at $x=a$ iff $f(x)≤f(a)$ ∀$x$∈ Domain of function.
So overall we can say , when we talk about local minima/maxima we compare it with nearest points and then declare nature of function at that point but when we talk about Global minima/maxima we compare it with whole domain.
Global minima $⊆$ Local minima and similarly Global maxima $⊆$ Local maxima