Although this thread comes up all the time, you can't blame a new guy for asking because the search function excludes the terms "S4" and "S5" because they're too common.
I agree with all the differences mentioned above except one: I've never heard that the wiper switch relays were more substantial in S5 vs. S4. Many S5 cars experience the same wiper switch failures that S4s do. Note that the superior rubberized plastics in the S5 interior are pretty much limited to the radio surround and shifter surround bezels. The dash demister vents, door vents, passenger side kick panel, rear speaker grilles, etc. are all just about as brittle as the equivalent S4 parts. You can swap the two rubberized pieces from an S5 into an S4.
Many of the differences amount to styling changes: trim, taillights, paint choices, wheels, interior fabrics and colors. Some are functional: different types of LSD, slightly higher horsepower levels in S5 vs. S4, slightly heavier weight in S5 vs. S4, 4-lug cars only available in S4, airbag in 90-91 'Vert, none in '88 (some '89s did have it, I believe). Really there are too many differences to list. I've owned both and I'm still discovering differences.
When shopping for a TII, you'll probably find far more S4s than S5s. This is because S4 cars outsold S5s by a wide margin. This is partly because sports cars usually sell best when their designs are fresh, and partly because the Miata probably stole some buyers away from the RX-7. For whatever reason, S5 TIIs are rarer than S4s.