What are the different shipping methods on ebay?

That depends which ebay you're talking about:

ebay.co.uk : Royal Mail International Signed
ebay.com : United States Postal Service (USPS)

Other countries may use their own courier service and the following may be offered as well:

1. TNT
2. Parcel Force
3. DHL

I'm assuming you're buying from abroad to be delivered in Mauritius.

You get only two types of shipping i would say.., free and paid.
But you have to compare because usually free shipping could be somewhat be a little more that you would pay.i;e seller already putting the price in the item for shipping.