Ha! I was right

Well, sjkas­abi, Wiki­pe­dia agrees with me:

Note that the solidus and vir­gule are dis­tinctly dif­fer­ent typo­graphic sym­bols with decidedly dif­fer­ent uses. The solidus is sig­ni­fic­antly more oblique than the vir­gule. The char­ac­ter found on stand­ard key­boards is the vir­gule and while most people lump the two char­ac­ters together, (and when there is no altern­at­ive it is accept­able to use the vir­gule in place of the solidus,) they are dif­fer­ent. The solidus is used in the dis­play of ratios and frac­tions, while the vir­gule is used for essen­tially any other tex­tual purpose.

Source: Wiki­pe­dia

That does­n’t help me on the cor­rect name for a | though… but I’m work­ing on it!