No.. they are different

Hence why hosts that offer unlimited bandwidth are lying, but there is some truth in 'unlimited transfer'.
Transfer is the amount. Bandwidth is the width of the 'pipe'.
Take a car on a 2 lane road going 100/hr and 4 cars going 100/hr on a 4 lane highway side by side.
Both are going the same speed. They will get to their end destination in the same amount of time. That is transfer.
Bandwidth is how many cars can do it at the same time.
Just like some home connections may have a 4 meg/s connection but the ISP secretely limits the open connections to say 30. So they can only have 30 connections open.
If you go and get a high cost business connection for 4 meg/s you may be allowed 100s of simultanious connections.
The business connection would allow you to send alot mroe data.. it would appear fast as there isn't that same bottleneck in effect.
That might not make much sense.. but I tried :p