The difference between Minimal and Minimum

When used as adjectives, minimal means the smallest possible amount, quantity, or degree, whereas minimum means to the lowest degree.

Minimum is also noun with the meaning: the lowest limit.

check bellow for the other definitions of Minimal and Minimum

Minimal as an adjective:

The smallest possible amount, quantity, or degree.
Minimal as an adjective (arts):

characterised by the use of simple form or structures.
Minimal as an adjective (music):

characterised by the repetition and gradual alteration of short phrases.

Minimum as a noun:

The lowest limit.

Examples:

"We prefer candidates with a minimum of 4 years experience in the field."

"We need a minimum of three staff members on duty at all time."
Minimum as a noun:

The smallest amount.

Examples:

"He always tries to get away with doing the minimum."

"Please keep noise to a minimum after 11 o'clock"
Minimum as a noun (astronomy):

A period of minimum brightness or energy intensity (of a star).

Examples:

"The Maunder minimum of the Sun reportedly corresponded to a period of great cold on Earth."
Minimum as a noun (analysis):

A lower bound of a set which is also an element of that set.
Minimum as a noun (statistics):

The smallest member of a batch or sample or the lower bound of a probability distribution.