Armature and terminal voltages in DC machines
Firstly, the graph at the top of your inserted diagram is for an AC motor yet, the question is about DC motors. I assume that was an oversight.

I just copied the whole page. I mean by chance it came to be on the
same page. I thought this way it's more respectful to the author!!!

No, I don't think so; it just led to confusion. You can respect the author by providing proper attribution as you have partially done at the base of your question.

Do you agree with my interpretation?

There is an error and it's how you have represented \$V_a\$ in the DC motor - it is in series like this: -

The error you made is assuming that \$V_a\$ is in parallel with the armature inductance \$L_a\$. The back emf in that inductor must always be shown to be in series with the inductor.
And, for the generator it is exactly the same; all three components are in series. This also means that when unloaded, \$V_a\$ exactly equals the output voltage \$V_T\$. When loaded then \$V_a\$ is going to be bigger than \$V_T\$.