The phases or periods in a training plan serve the purpose of focusing attention on certain qualities that make up the bulk of that period’s training.
The Base period in both our plans and the TP ATP is the period where you are trying to increase your work capacity in the several fundamental qualities that make up your event. So Base = Base in TP and UA plans. Our Transition period seems to overlap with the Transition period in the TP ATP but I am not sure what differentiates their Preparation from our Transition. Their Build 1 Period is similar to our Specific Period. The training begins to model the event you are training for more closely. Not so sure about Build 2 other than it looks like intensity goes way up.
Keep in mind that our ATP graphic is meant to provide a qualitative general idea, hence the colors. The TP ATP you attached in your post is meant to be a quantitative representation of the actual training volume and intensity.