There are basically two ways to finish a short sleeve on a golf shirt. For years, a very popular way to finish the has been with a band.

The banded sleeve has been around for decades. It has been the most popular style for finishing off a polo shirt.
The advantage of a banded sleeve is that is finishes off the sleeve. It creates a uniform look around the arm.
Recently, customers have been asking for short sleeve golf shirts that are finished with a simple hem on the sleeve.

The hemmed sleeve is less constrictive, creates a more open look. As hemmed sleeves first became available, they were mostly found on higher quality golf shirts. But shirt makers are now introducing them on golf shirts of all price points because buyers have requested it.
The difference in these sleeve styles really comes down to personal preference. Is there any real difference in performance? No. It is more about the look you like and the comfort of the shirt.