I am wondering if there is a relationship between a zone density and residential wealth? For example, do high wealth Sims only live in high density areas?
There is no relationship. There are LD, MD, HD versions for LW, MW and HW. All residential buildings start at LD and move up to HD as they accumulate happiness (and as space and roads permit).
Also, how do you get high density industrial? I've tried placing parks around my industrial zones but I did not notice any change in my density.
HD industry is 8x4, which is to say, 8 street widths must adjoin the road - it is twice as long as MD industry.
For comparison: LD industry is 4x2. MD industry is 4x4.
You might be trying to get High Tech industrial. T1 is the starting tech level. T2 is reached by students attending Community College. T3 is reached by students attending University (or by Vu Tower). You can go directly from T1 to T3. Refer to the tech level dataview (the gear icon).