The difference between Ability and Capacity

When used as nouns, ability means suitableness, whereas capacity means the ability to hold, receive or absorb.

Capacity is also adjective with the meaning: filling the allotted space.

check bellow for the other definitions of Ability and Capacity

Ability as a noun (obsolete):

Suitableness.
Ability as a noun (uncountable):

The quality or state of being able; capacity to do or of doing something; having the necessary power.

Examples:

"This phone has the ability to have its software upgraded wirelessly."

"This wood has the ability to fight off insects, fungus, and mold for a considerable time."
Ability as a noun:

The legal wherewithal to act.
Ability as a noun (now, limited to, _, Scottish, _, dialects):

Physical power.
Ability as a noun (archaic):

Financial ability.
Ability as a noun (uncountable):

A unique power of the mind; a faculty.
Ability as a noun (countable):

A skill or competence in doing; mental power; talent; aptitude.

Examples:

"They are persons of ability, who will go far in life."

"She has an uncanny ability to defuse conflict."

Capacity as a noun:

The ability to hold, receive or absorb
Capacity as a noun:

A measure of such ability; volume
Capacity as a noun:

The maximum amount that can be held

Examples:

"It was hauling a capacity load."

"The orchestra played to a capacity crowd."
Capacity as a noun:

Capability; the ability to perform some task
Capacity as a noun:

The maximum that can be produced.
Capacity as a noun:

Mental ability; the power to learn
Capacity as a noun:

A faculty; the potential for growth and development
Capacity as a noun:

A role; the position in which one functions
Capacity as a noun:

Legal authority (to make an arrest for example)
Capacity as a noun:

Electrical capacitance.
Capacity as a noun (operations):

The maximum that can be produced on a machine or in a facility or group.

Examples:

"Its capacity rating was 150 tons per hour, but its actual maximum capacity was 200 tons per hour."

Capacity as an adjective:

Filling the allotted space.

Examples:

"There will be a capacity crowd at Busch stadium for the sixth game."