Maximal vs. Optimal — What's the Difference?

Of, relating to, or consisting of a maximum.

Most favorable or desirable; optimum.

Being the greatest or highest possible.

The best, most favourable or desirable, especially under some restriction.

An element in an ordered set that is followed by no other.

(artificial intelligence) Describing a search algorithm that always returns the best result.

Largest, greatest (in magnitude), highest, most.

The best of its kind

(mathematics) The element of a set with the greatest magnitude.

Best possible; most desirable; optimum; as, the optimal concentration of a drug.

(mathematics) Said of an ideal of a ring or a filter of a lattice: that it is as large as it can be without being trivial (improper).

Most desirable possible under a restriction expressed or implied;

(logic) Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.

The greatest or most complete or best possible;