A guarantee:

Is usually free
It’s a promise to sort out any defects with a product or service within a fixed period of time
It’s a legally binding contract, even if you didn’t pay for it
It must explain how to go about making a claim in a way that is easy to understand
It should add to, not take away from, your rights under consumer law
It works whether or not you have a warranty

A warranty:

A warranty is like an insurance policy for which you must pay a premium.
Sometimes it’s called an ‘extended guarantee’.
It might cover a longer period than a guarantee, and it might cover a wider range of problems.
A warranty is a legal contract, so you can take the company to court if they don’t honour it.
The terms of the contract should be clear and fair.
Having a warranty doesn’t diminish your rights under consumer law.
A warranty can run alongside a guarantee.