Any jewellers?? Help with ring size mystery

[Cathpot]

I damaged an enamelled ring to the point it couldn’t be reshaped . The shop I bought it from offered to make me a new one at half price. I live the other end of the country to the shop , so I went into a local jewellery shop and asked them to measure my finger. They said I was an M. The old ring went off in the post and the new one turned up. It was far far too small. I presumed the local shop had made a mistake . The ring shop were very good about it and offered to change it . I went to a different jewellery shop and they told me I was N and a half. As I left the shop the man said~ that’s finger size by the way.
So then I measured my finger size in mm - 65mm. I look this up and it says that makes me size W. I call the ring shop who agree the mm size suggests I am a W and have no explanation as to why two different shops have measured me M/N. Are there two scales??

62mm? Jeez. Even my plumber husband's sausage fingers are a lot smaller than that

What a lovely helpful comment that is.

The style of the ring will make a difference. If the band is quite wide it will need to be a bigger size than a really thin band. So if you're measured with a thin ring sizer and the actual ring is wider then it wouldn't fit. You need a cheap ring as close in shape and size to the actual ring to get a true size.