The history of typefaces and the peculiar references to size and space goes back to the origins of moveable type.
Terminology changes
Nowadays most people use the terms ‘font’ and ‘typeface’ interchangeably. That wasn’t always the case.
The space between each line of text has two origins. The first was, as explained here, was from printing, and was referred to as leading.
The second comes from typewriters. They had fewer options in terms of line spacing, so we get single, double and one and a half lines as options.