The punctuation symbol ( / ) has also been called a virgule, a stroke or an oblique in pre-computer days, although they are mainly British English terms that are fading (I think) in the face of the word slash. To me they are now the slash and the backslash (but I grew up calling the first a stroke). However some feel "slash" might be misinterpreted as a backslash and invented the term "forward slash" and it is sticking!
The other one, the backslash ( \ ), is not a punctuation mark but a symbol used in defining computer (file) locations.
I say slash and backslash in computer contexts. In other contexts, I tend to say stroke(/). The other day, I heard it called oblique stroke.
(The backslash is only encountered in computer contexts only, as far as I'm aware.)
When reading it out, you might also say different things depending on text. In the context of music chords (say G/A), I might say over (G chord over A). In some contexts, I might say per (2 m/s = 2 metres per second). For marks or scores, I might say out of. And so on.