A spell scroll looks like a scroll
The DMG explicitly describes scrolls on page 139, in the section on magic item categories:
SCROLLS The most prevalent type of scroll is the spell scroll, a spell stored in written form, but some scrolls, like the scroll of protection, bear an incantation that isn't a spell. Whatever its contents, a scroll is a roll of paper, sometimes attached to wooden rods, and typically kept safe in a tube of ivory, jade, leather, metal, or wood.
All scrolls (that are magic items) are rolls of paper. A spell scroll (the magic item) is a type of scroll. Therefore, a spell scroll is a roll of paper.
In addition to that, from the spell scroll description on page 200 of the DMG, we also know that:
A spell scroll bears the words of a single spell, written in a mystical cipher.
The more specific rules text of spell scroll does not make other statements about the look of the scroll. There is nothing specific in the core rules to override the general description of scrolls for spell scrolls.
Materials
By the strictest interpretation of the definition in the DMG, a spell scroll cannot even be written on papyrus, parchment, or vellum, it must be paper. Even though the name paper etymologically comes from papyrus and both are plant based, papyrus is not the same as paper. Parchment or vellum, both used historically for writing on, are made from animal skin and would only count as paper in the sense of a thin material used for writing on.
In the optional rules for scribing a spell scroll from Xanathar's Guide to Everything, one of the complications is: "The rare parchment you bought for your scroll has a barely visible map on it.", which indicates even the publishers assume parchment as a typcial material to scribe scrolls on. Therefore, it could be reasonable to consider a wider definition of paper. Your DM, if they prefer to allow these or even more exotic materials, may interpret or overrule the written rules text accordingly, see page 4 of the DMG. I certainly would do so in my home game.
illustro futher has pointed out that in Storm King's Thunder, spell scrolls can be found written on vellum. In this case specific beats general, and those specific spell scrolls override the strict reading of the ones prescribed by the rules.
The creation of magic items by the PCs, including the scribing of scrolls, is in the purview of the DM. If a DM allows the players to scribe scrolls, he might also allow them to use other materials; at least for common materials like papyrus or parchment this is highly unlikely to have any negative effect on the game.
Other scrolls with spells
The reference you recall about spells being possibly written in many places might be the one from the decription of the spellbook, on page 114 of the PHB:
The Book’s Appearance. Your spellbook is a unique
compilation of spells, with its own decorative flourishes and
margin notes. It might be a plain, functional leather volume
that you received as a gift from your master, a finely bound
gilt-edged tome you found in an ancient library, or even a
loose collection of notes.
Thus it is possible to write spells on any kind of substrate. You could have non-magical scrolls with spells written on them, (see the "loose collection of notes" above), and then would have a nonmagical scroll with a spell on it, in the same way a spellbook is not magical, but these scrolls would not be spell scrolls.
Contrast to other answers
Several of the other answers make well researched cases for ignoring the rules as written, which I sympathize with. It seems inane to not be able to write a scroll on parchment or vellum, and even the publishers themselves do not care about their own rule in the adventures they publish.
Neither is it harmful to allow more exotic expressions of the concept of a one-time consumable spell that traditionally is rendered as a spell scroll, to the contrary, it can be full of flavour. Spell fetishes, spell figurines, spell prayer beads, spell feathers, spell tattoos... the possibilities are endless and fun.
I never the less cannot in good faith answer that a spell scroll, as described by the rules, is anything other than a scroll made of paper. That is what the rules say, and it does not matter if I like it or not, or if they ignore it themselves. It will remain so, until WotC issues errata on the text.