What is the difference between Waive and Wave?

What is the difference between Waive and Wave? :

Waive :

1 ) Not insist on something in a particular case


Do not waive the relevant rules.

We have decided to waive the age-limit for application in her case.

Wave :

1 ) Move regularly and loosely to and fro or up and down

A flag is moving in the breeze.

Branches are moving in the wind.

2 ) Move one’s hand to and fro and up and down in order to attract someone’s attention

She waved to me when she saw me.

They waved at us from across the room.

3 ) Cause to move up and down or to and fro in order to make a signal or give a greeting

He waved a hand at me.

He came out waving the documents at the crowd.

They waved to us to stay where we were.

4 ) Give a greeting by waving one’s hand

I waved her goodbye.

They waved goodbye to us.

5 ) Form a series of curves

Her hair waves beautifully.

6 ) Cause something to form curves

She has had her hair waved.

Wave : (noun)

1 ) Ridge of water

The storm whipped up huge waves.

2 ) Act or gestures of waving

She greeted me with a wave.

The magician made the rabbit disappear with a wave of his hand.

3 ) Sudden, temporary increase and spread of something

A mounting wave of anger and dislike rose within me.

There was a crime wave in certain parts of the city.

There was a heat wave in the recent past.

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