My understanding is:
Static--mentally abstracted, dealing with bits and pieces.
Dynamic--mentally immersed, adapting and adjusting "things" as they come in. ("Things" are relationships for Pi, and systems for Ji.)
IOW, Static is analytic, Dynamic is synthetic. I believe credit goes to labcoat for that one, but I don't want to claim he's been saying potentially stupid things
I can compare Si and Ti like that. Ti is piecing together things, having this framework, and connecting either systems of dots, or the dots themselves; Si is an immersed process, adapting myself to a constant stream of stimuli.
Ti is like arranging individual piecewise photographs into a panorama, Si is like watching a YouTube video and deciding when I need to buffer, or change the volume, or the screen settings on my monitor, so that everything is perfectly adapted For Maximal Enjoyment/immersion/whatever.
I still think deep/shallow or heavy/light are potentially bad names though, but that's no grounds for criticising the dichotomy itself. I'm not sure if you are though, Jonathan.
EDIT
I could also see how light/heavy applies to the Socials, and especially from the P.O.V. of one looking at the other.