Jacobi coordinates - definition

I became quite confused about Jacobi coordinates. Until now I've been used to them as the coordinate system, where coordinates are vectors pointing to the center of mass of previous "subsystem", as we can see in the picture


[![enter image description here](https://i.stack.imgur.com/OPWoq.jpg)](https://i.stack.imgur.com/OPWoq.jpg)


Also, they're described in the same way in the [Wikipedia](https://en.wikipedia.org/wiki/Jacobi_coordinates).


But today I've met two colleagues, who were talking about Jacobi coordinates in 3-atomic system as about "vector-vector-angle", looking like this


[![enter image description here](https://i.stack.imgur.com/0OtSN.png)](https://i.stack.imgur.com/0OtSN.png)


with descriptor set being $\left(R,r,\cos^2(\Theta)\right)$.


Is this coordinate system also called Jacobi coordinates? And if it isn't, what's its real name?


