Did Apple change the display adapter from MacBook 2006 to MacBook Pro 2010?
I thought they were the same, (similar size) but they actually differ.
Do I have to buy a new adapter?
The Output port from early MacBook (and MacBook Pros) was a mini-VGA, later a mini-DVI port and various accessories were available to connect regular size VGA displays. 15" and 17" PowerBooks had full-size DVI outputs as far as I can remember.
Recent MacBook models use a smaller mini DisplayPort. Apple itself offers different adapters to transform the mini DisplayPort into VGA, DVI, or HDMI. If you need a VGA adapter (like you say in your question tag), you are looking for this. If, on the other hand, you need to connect a DVI display, then this is what you want.
Apple laptops have gone through the following display adapter transitions
The MacBooks never had mini VGA, they started with mini DVI, but earlier Apple laptops such as the iBook used mini VGA. Before they featured mini DisplayPort, early MacBook Pros used a full size DVI port.
Note that a Thunderbolt connector is backwards compatible with mini DisplayPort displays and adapters, and looks the same. It may seem as though there's been no transition in 2011, but the Thunderbolt port enables new functionality that mini DisplayPort did not have prior to 2011.