What is the difference between Air and Heir?

What is the difference between Air and Heir? : 
Air : 

( 1 ) Mixture of gases surrounding the earth and breathed by all land animals and plants

Let us go out for some fresh air. 

( 2 ) The earth’s atmosphere – open space

He likes to be in the open air. 

( 3 ) The earth’s atmosphere in the space where aircrafts fly

Send goods by air. 

I always travel by air. 

The site of old fort is clearly visible from the air. 

( 4 ) Impression given, appearance or manner

He smiled with a triumphant air. 

That place has an air of mystery. 

Heir : 

( 1 ) Person with legal right to receive property when the owner dies

Are you the heir to the throne? 

He is the heir to a large fortune. 

He made her his heir.