No. The MyTouch series and the G1 series are two completely different series within T-Mobile's Android services. The MyTouch was the original phone within that series and the G1 was the original in it's series. The G1 was actually the first Android phone ever released. The MyTouch and the G1 have striking similarities because the MyTouch was inspired by the G1. So, I guess you could probably call them brother and sister.
Also, don't really believe much of what you see online, especially with images. A lot of them are fan made and a lot of them are rumors. Such as the images for the "T-Mobile G3" which look like a Android version of the iPhone. (Which are totally fake, we have no information at this time about a T-Mobile G3). Only a select few of the images out there for the G2 are real images, unfortunately I am not allowed to post them on here, but I'm sure someone else will. It's not that you're not allowed to see it yet, it's just because it could jeopardize my job because of the fact that T-Mobile hasn't actually OFFICIALLY released it yet.