Why the difference?
Because the higher your line runs at, the more likely you are to reach a bottleneck somewhere else in the internet.
For most checkers, there is nothing mystical about them; they are not in a magic segment of the internet that cannot be overloaded by anything else - and they still have some limitations. When the biggest bottleneck in a connection is the user's own line at 8Mb or less, it is just that the other limitations don't often come into play.
If you have a BT-supplied connection, then the BT checker might be better because it can be routed entirely within BT's network. This would remove any ISP-based or Internet-based bottlenecks, but you may still suffer from bottlenecks within BT's network.
On balance, with faster speeds, the speed checkers become less useful at measuring your absolute top-end speed.