The two scales share a name and nothing else, which is the source of most confusion about old references.
The US scale
Twice the ABV, with no exceptions: 80 proof is 40%, 90 proof is 45%, 100 proof is 50%. US labels commonly carry both figures, and the ABV is the one that means the same thing everywhere.
The old British scale
100 degrees British proof was approximately 57.1% ABV. The definition came from the gunpowder test: spirit was "proved" if gunpowder moistened with it would still ignite, which happens at roughly that strength. The scale was abolished in the United Kingdom in 1980 in favour of ABV, but it survives in old texts and in the naval associations of overproof rum.
Why it matters when reading
A nineteenth-century British reference to 100 proof describes a considerably stronger spirit than a modern American one. The number is not comparable across the two systems.