Brush Knee Twist Step (called “Walk obliquely with twist step”, which was probably its original name) is a fundamental movement in all Tai Chi styles.
Chen Zheng Lei performing “Walk obliquely with twist step”:
The Yang style Brush Knee looks like a slightly simplified version of this. Here performed by Yang Jun, grandson of Yang Cheng-Fu :
And Sun Style looks like the Yang style, but with added steps. Here performed by Sun Peng who is Sun Lu Tang’s grandson :
The version I personally do is somewhere between the traditional Sun and Yang styles. It’s got a step, but it’s most like Yang. Here’s a little GIF showing me doing an application of Brush Knee Twist Step in push hands from the Tai Chi style I practice.
Here’s how it looks in my form (a Yang style variant from the Gu Ru Zhang lineage that had input from Sun Lu Tang).
Of course, there are many possible applications of this movement, and I’m just showing one, but hopefully, that gives some indication of the usage.