Syrup, jelly, must; it’s all Greek to me!

The main difference is texture: a jelly is firm and lumpy enough that you can hold it with the side of a knife and spread over something else (like a toast), but you'd have a really hard time pouring jelly over something by tilting the container. In the meantime a syrup is a thick liquid, so it's runny and you can pour it over.

Traditionally, the source of that difference in texture is a substance called pectin, found in plenty fruits. Grapes do have pectin, but once you squeezed them into juice most pectin went to waste with the pomace and skins, so even if you reduce the juice for defrutum it'll be still a runny liquid.

Must is simply grape juice, ready to be fermented into wine, although in Latin the word mustum also sometimes pops up for young wines. Additionally, in the context of Catholic masses it's grape juice suitable for communion.