I think you will find that Sagepay is a third party payment service, some companies use it to receive card payments. I have certainly paid companies using these services. paying is similar to using Paypal but you don't have an account with Sagepay like you do with paypal. The only difference as I understand it is that you don't get the same protections that you do when you pay normally direct with your card, although unless you are spending a huge amount I wouldn't worry too much. I have done many transactions using third party payment systems without any issues
When you pay using these third party payment services you don't normally do anything different than you do when paying direct with your card. When you are paying the web site may say something like "we are transferring you to our payment system or similar, you just enter your card details, it takes your payment them transfers you back to the original web page.