These are my definitions of both of these terms. I will start with old school cheap.

OLD SCHOOL CHEAP

An old school cheap extreme example is like when a person washes paper plates. That
is an example of the person I live with my mother. Old school cheap is also good as long
as you know that.

STRATEGICALLY CHEAP

I am a very Strategically Cheap person. Using the example above,
I would do lots of research and find out which dishes actually break
the least, and I would buy those dishes and use them for the rest of my life.
The dishes we have right now are dishes that my mother had when we moved
in here in 2020 and because no one else comes in this house, we have had no
broken dishes at all here so far.