Have you noticed nowdays how many prologues are around? They are demo, but the call them prologues.
Prologue basically means the beginning of a story, intro, etc.
I think the difference in terminology varies based on if its actually the opening or "first segment" of a game, usually I think of it as Chapter 1 myself.
You don't see this with AAA companies often because the "Prologue" is designed to waste almost your entire 2 hour refund with storyline so you can't actually decide if you like the game
That or they just start you mid journey and let you taste the basics like battle (with skills you would never acquire in a demo) and movement...since your likely already a fan of the series itself or the characters in some way shape or form.
Smaller dev teams usually don't have that luxery either because the beginning is all thats complete, or because they obviously didn't pay to license characters from well known shows, comics, or games.
Its ironic you mentioned this after my Trails Of remark, because Trails from Zero and Trails of Azure break this trend...being an accepted and modified version of a fan translation by Geofront.
Regardless, no demo was even needed for this game or series, although during the fan translation process I believe you could play the game to some extent.
btw I go to take a rest

cya later
Night bro, rest easy
