Yes, AOL is part of TT, but AOL sell and provision its BB products much differently.
AOL usually provides a
capped 'Up to 8 Meg' product running over ADSL2+ whereas TT will provide the uncapped ADSL2+ product capable of running up to its full 24 Meg. This would only be an advantage if your line length to exchange were < 3 km.
If you were to provide the the router stats asked of you and which exchange you are on it would end all the speculation evident in this thread on both sides. If you don't know which exchange use:
http://www.samknows.com/broadband/exchange_search and post the URL of your exchange page.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC