The difference is:

• order_id is the internal Magento order ID (database table auto increment id)
• increment_id is the ID which you communicate to your customer
• quote_id is the internal quote id (When user add product to cart those are added in quote , after checkout success quote is transferred to order)

The difference is:

• order_id is the internal Magento order ID (database table auto increment id)
• increment_id is the ID which you communicate to your customer
• quote_id is the internal quote id (When user add product to cart those are added in quote , after checkout success quote is transferred to order)

Why they are different

order_id and quote_id needs to be different because they refers to the different table(or different object, order_id refers to order object while quote_id refers to quote object), increment id is different as it allows you to show a different order-id with prefix to the customer