Have an existing 100 amp service. Wish to install a 70 amp sub-panel. What size wire should be used? Distance to sub-panel is 45 feet.

#4 will work, #2 will reduce voltage drop.

#2 is extreme overkill at only 45'.
Voltage drop is not even close to an issue at 45', even at full load amperage.

Why do you need 70A? Using #6cu you can go with 60A and the wire will be much cheaper. If you do go with #4 you can use a 90A feeder breaker, or even 100A in some cases.

If you must have a 70A breaker then you must use #4cu.

If this was my Shop, I like a little overkill. Plus, I could easily upgrade to a 100 Amp Panel. I have no idea of other losses/lengths involved.
#4 will work.