I am fairly happy with my buttonholes on the whole, but there is a fundamental difference that I see with professional ones and I can't work out what I am not doing quite right.
Pictured below are 1. One of mine and 2. One on a velvet Savile Row DJ I have (not made for myself sadly):
The stitches seem much tighter, closer together. It's also much stiffer. The thread might also be finer I think?
If I try to pull stitches tighter it just makes the hole deformed. Any ideas?
When I made my first suit at Henry Pooles I asked Jinny to put in my buttonholes because she was considered the best.
That coat now hangs in my classroom as an example of what can be achieved. I am sure I could show at least one or two holes of that quality, but 13 on one coat would be a stretch.
It's most likely a finer thread, as you suspect.