I could imagine that the resource usage or internals of how the backup takes place have been improved upon. However, there is no real difference - a full backup is a full backup. You will not be able to restore a SQL 2005 backup to a SQL 2000 server, they are not backwards compatible. A SQL 2000 backup **can** be restored to a SQL 2005 server though.
What happens during a full backup is that first are the datapages written to the backupdevice. During the backup, no new data is written to the datafile, instead all transactions are written to the transaction log. The parts of the transaction log that was written AFTER the backup started are written to the backupdevice, and then SQL Server writes these transactions to the datafile. This is - as far as I know - the same between SQL Server 2000 and SQL Server 2005.