The Cap’s first pair of boots are the retro, red ‘pirate style’ boots. The second pair appear to be standard WWII US GI type brown leather combat boots, as seen below:
However, note the sole visible in the following image:
This appears to be a black or brown Mini-Vibram sole. The first Vibram soles were released in 1937, though they were an Italian product, which makes it unlikely that the above boots are replicas of period Allied combat boots. Either these are not-very-accurate repro US GI boots, or they have been re-soled; perhaps to add a bit of height. You’ll note that Rogers’ bootheels are slightly taller than Bucky’s.
The third pair are modified WWII US GI ‘jump boots’ with a fabricated leather cuff and buckles attached at the top of the boot. Those are worn with the new Howard Stark-made suit for all the following action scenes after the POW rescue.