Ancient *slash* → new *back-slash* → disambiguating retronym *forward slash*
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Ancient Roman coins - Solidus and Denarius.
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The *slash* character came first, with a different formal name *solidus*. This name comes from Latin and was associated with coinage - hence (I guess) it's use in writing down prices in older currencies: `10/6` was quite a common notation for prices in British currency pre-decimalisation. The solidus mark probably indicates the first number is units of solidus, the second of denarius. Or in the British case: shillings and pence. Note common first letter abbreviations s and d were used in Britain (also £ is L for Latin libra).
The slash (or solidus) was around for a very very long time before the reversed version was invented. The reversed version therefore acquired the more informal name back-slash to indicate a reversed form of slash.
The name "forward slash" has probably evolved since the general public started to use computer keyboards incorporating two characters that look like a slash. There was a need to disambiguate *slash* for people who didn't learn about computers in a formal teaching context.
1899 - Adler typewriter company.
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[![enter image description here][1]
<sup>\- Photo © Dake - CC-by-SA 2.5</sup>](https://en.wikipedia.org/wiki/German_keyboard_layout#/media/File:Typewriter_adler1_keyboard.jpg)
Slash, but no backslash.
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1963 - American Standard Code for Information Interchange (ASCII)
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[American Standards Association (ASA) X3.4 subcommittee](http://worldpowersystems.com/J/codes/X3.4-1963/)
/ slant
...
\ reverse slant
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1991 - [Unicode consortium](http://www.unicode.org/charts/PDF/U0000.pdf)
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002F / SOLIDUS
= slash, virgule
005C \ REVERSE SOLIDUS
= backslash.
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So it is clear that the name backslash was introduced to indicate a novel character that was the reversed version of a long established character.
The name forward slash therefore subsequently became needed to disambiguate the name for the earlier character.
[1]: https://i.sstatic.net/LeN5n.png