many people think the two are one and the same thing, but they're not.
A guarantee is traditionally a promise - that something will be done, or some benefit bestowed. In our context it's usually offered by the manufacturer of an item, and will be valid for a set period - often one or two years. The terms of a manufacturer's guarantee normally extend to covering the cost of replacement parts (or the entire item) if they/it should prove to be defective within the stated period. A manufacturer's guarantee is in addition to (not in place of) your right of recourse to the retailer under current consumer legislation.
A warranty (again in our context) is effectively an insurance which comes into force on payment of a fee by you to the retailer. In fact the warranty will be underwritten by a finance company - a third party - and the retailer gets a portion of the fee in return for getting you to sign up and handling the paperwork. The warranty will be in addition to your rights in law, and also to the manufacturer's guarantee. Warranty claims are usually subject to certain terms and conditions, and you must read those carefully before committing yourself.
Many people in the consumer-advice business have warned that warranties are often highly-priced and totally unnecessary; you get adequate protection under the law, and the cost of extending your protection beyond the statutory period is far and away more expensive than the cost of paying for any likely repairs. In addition, the road to satisfaction under a warranty claim is often a stony one, and stories abound of people who had great difficulty in getting a claim settled.
In the end it's your choice, but if you do pay for an extended warranty make absolutely sure that you've read the small print thoroughly, and that you understand precisely what is (and isn't) covered in the event of a claim.