Mature, matured, ripe, mellow, adult, grown-up are comparable if not often interchangeable because they all bear the same underlying meaning "fully developed."
Mature, in its basic use as applied to living things, stresses the completion of development; as applied specifically to persons, it usually implies attainment of the prime of life, when a person is at the height of his powers, physically and mentally.
As applied to things, mature usually equals matured, which implies the completion of a course, process, or period; thus, a matured plan is a fully thought-out plan; a matured wine is one that has been allowed to age properly; a matured note is one that has reached the date when payment is due.
Ripe, though it implies maturity, stresses readiness for use or enjoyment; in its basic sense it is applied chiefly to such things as fruits ready for eating, grains or vegetables ready for harvesting, or seeds ready to germinate. In extended use it often connotes merely readiness or full preparedness for action, activity, or use.
Sometimes, however, ripe connotes one or more of the characteristics of ripe things, especially ripe fruits, such as ruddiness, plumpness, or richness.
Mellow stresses either such agreeable qualities associated with ripe or slightly overripe fruits as softness, tenderness, sweetness, or the loss of their opposites, the signs of immaturity, such as hardness, harshness, or bitterness.
Adult is the equivalent of mature in its application to the physical characteristics of living things. It presupposes, however, a clearer line of demarcation, especially when used of human beings. An adult person physiologically is one that has passed beyond adolescence; in law, he is one that has attained his majority.
In extended use adult implies the attainment of that point in development where the weaknesses of immaturity or of imperfection are surmounted.
Grown-up is sometimes used in preference to adult when an antithesis to childish is needed.