pp and ebay are basically the same site, if you win an auction a single click will take you to paypal's site where you can put in your CC or pay with existing funds right away. The pay by email thing is confusing, it just means that if someone sends you money through their site, or you send money to someone they will send you an email telling you that it has happened.
They are just like a bank, but with no tellers /ubbthreads/images/graemlins/smile.gif
They also want to link your online account to a real bank account. Once you do that you can transfer funds via their website back and forth between the 2. So if you make a lot of money selling stuff via eBay you can transfer the money to your real world account.
Many people, including me, dont really like having Paypal linked in to our daily living accounts and recommend that you open a separate checking account not linked to any of your existing accounts so that if a horrible error were to be made by them they couldn't' clear out your living money.
So, specifically, no, you dont need to send an email or cut and paste the bid info. When you win the auction there is a link to "pay with paypal" and you just click it and it will setup everything else for you.