Or, to be more precise: Solidus, Virgule, Backslash

When we speak of the ’slash’, we are speaking in the vernacular. Properly speaking, in typography, there’s no such thing as one.
Consider the gallery above. From the right: the virgule, the solidus, and the backslash. The first two are common to typography; the last one sees often if using a computer. The differences between the first two are simple, and between the last one and the rest obvious. Each one has a particular use.
The one that’s most close to a 45º angle from the verticle is the solidus. Its a fraction bar; with a superior and inferior digit it is used to construct fractions on a line that look more like fractions and not like two digits and a slanted mark strung together.
It comes to us from from the Roman Empire via England. The solidus was originally a Roman coin, introduced in AD 309; there were 72 of these to the libra, or the Roman pound. The British based their currency system on the Roman, and through the middle of the 20th Century British currency was composed of pounds, shillings, and pence, written £/s/d; the slashes separating the amounds became known as the solidus.
Since decimalization of the British currency system, the solidus is now best used to express fractions in type.
The virgule is a gift of the Medieval scribe. It is believed that it was first used to indicate a pause in text, and thus could be an ancestor to the comma.
Latterly, the virgule serves a variety of uses. Not only does the mark form the fraction bar when all glyphs in a fraction share the baseline (known as a level fraction) but it serves a separator in certain contexts, such as between files and folders in a Unix filesystem path, or between lines of verse when typeset as prose.
The backslash is a johnny-come-lately to the family, a gift of the modern computer. Most commonly it can be seen as a separator character in a Microsoft Windows command line file path. For example, A document in a Window’s user’s home account might be:
C:\Documents and Settings\Me\My Documents\Report1.doc
There is currently understood to be no real typographical usage of the backslash other than what technology calls for.
The use of the marks should be obvious from their descirptions. Most appropriately, one should not use a solidus where a virgule is called for, and vice versa. A solidus-based fraction in type looks more readable; at smaller sizes, a level fraction may be more readable.
Formerly, a solidus-based fraction had to be cobbled together from the solidus and the numbers involved; only common fractions such as ¼, ½, and ¾ were included in standard sets. The advent of OpenType, with its sophisticated feature set, has made things much easier on the digital typographer; in Adobe InDesign, as an example, all that is necessary is to set the numbers and mark (either solidus or virgule) in a string, highlight the string, and selected “Fraction” from the OpenType item on the Character palette flyout menu, and the string will be converted to a solidus-based fraction automatically.
Reference: The Elements of Typographic Style, version 2.5, Robert Bringhurst


it’s interesting that you posit the virgule as being perhaps an ancestor to the comma because ‘virgule’ means comma in French.
Thank you for that follow-up, and actually, I meant to try to track down the roots of virgule. My research suggested that the virgule desceded from a medieval pause but I couldn’t quite find where the word actually came from.
Thanks again…this is great!
DESIGNORATI
What is the use of u+2044 “fraction slash”?