Inability = lack of ability, incapacity

• He expressed his inability to accept such a revolutionary idea.
• I am sorry to inform you my inability to attend the meeting.
• He is very sad about his inability to help the orphanage.
• Basically, it was her inability to give the team the best available coaching.

Connected usages – able (opposite) unable.

• I can’t help you! (The most blunt way of refusal of help)
• I cannot help you. (Moderate way)
• I am unable to help you (polite way)

Disability = ailment, disease, affliction etc.

• The orphanage takes special care about children with severe physical disabilities.
• The house will be made accessible for people with disabilities.
• The government should take measures to provide public amenities for people with disabilities.
• Children with learning and behavioral disabilities should be given special care and attention.

Connected usages: Disabled = people with physical disabilities.

(Note:  Now there is a general tendency not to use the word ‘disabled’.  Instead, the word ‘differently abled’ is popularly used in order to avoid the humiliation to the person concerned. Similarly you can see the the word ‘undeveloped nations’ is totally avoided in formal situations and instead ‘underdeveloped nations’ is used.