Sync essentially syncs your contacts and other things with Google and other services. You may see all accounts on your phone by visiting Settings > Accounts and Sync
The Sync part of Android syncs things such as Documents, Contacts, and other things to services such as Facebook, Google, Ubuntu One...
When the device "syncs", it syncs the data from your phone onto the service's servers. That way if you switch phones, if your new phone would have Syncing capability, you could retrieve your contacts and documents back to the phone. The syncing part of Android is also simplistic in a way too... Just add the account, turn on Auto Sync, and your done.
The "Auto Sync" feature can be changed from Settings > Accounts and Sync... That setting basically means that it will sync your device with the service's servers. If you turn Auto Sync OFF, you will have to go into Settings > Accounts and Sync and Sync the Accounts manually by tapping on them and tapping the menu key and selecting Sync Now.. This feature is good for those with limited data or restricted data on their Wireless Service Plan. I recommend keeping this option on when you have Unlimited Data that way your device will always be syncronized with the server's.
As far as the question for Facebook, Android always does that. It pulls up the name of the contact followed by the number.. not just from Facebook...
