[OT] What field (if any) of math am I looking for?

I'm 60+ and using Maxima to attempt to review math I "took" as an 
undergrad decades ago. My use of formal math terms will leave much to be 
desired.

In an engineering group, there was a question of comparing the "shape" 
of plots of observed data. The discussion got tangled in "where did data 
come from" rather than whether or not one short sequence (tens of 
points) in some sense had the same "shape" as another sequence.

I attempted to recast the problem

Given pairings of datasets ( ALPHA  BETA ), ( BETA GAMMA) etc
is there a measure ( OMEGA(x,y) ) such that

OMEGA(ALPHA(i), ALPHA(j)) always greater than OMEGA(ALPHA(i), BETA(k))

Some test cases

ALPHA [sinc(x), 1/x, Dirac delta, Kronecker delta, decaying exponential]

BETA [rising exponential, x**2, x**4]

GAMMA [sin(x), square wave, traffic thru a traffic signal]

I would suspect a child might group these that way.
Is there a field of math that might attempt to do that?

Thank you for your time.