I am looking at motors right now and notice some are labeled 208-230 and some are labeled just 230.
I do not need a lecture on the difference between star and delta. I am aware that tap to tap is 230(ish) on delta, and tap to tap is 208(ish) in star services. I've worked on both. When I was a kid we converted our grocery store (when we expanded it) to star because my dad believed is was more efficient and cost less to operate if we kept the load pretty well balanced. I don't know if he was right or not. I'm just familiar with the practical applications. I was the one maintaining our refrigeration equipment by my mid teens.
What got me is that most of the 208-230 labeled single phase motors are cheaper than the 230V labeled single phase motors. This makes no sense to me. 208-230V motors would need to be able to operate at slightly higher current which could theoretically mean marginally larger windings and/or better cooling. Why would they be priced lower? Why would anybody with 3 phase be running a single phase compressor anyway other than maybe as an emergency backup.
Your typical single phase or more accurately split phase small shop or home shop in the US will have 230V(ish) from L1 to L2. My service runs about 234-236.