See this post I did with /u/Xenophontheathenian that makes exactly that comparison.

u/Itsalrightwithme linked a useful post comparing early modern pike formations to ancient phalanxes, but I think we're still missing a crucial bridge: Spear infantry most certainly dominated the battlefield in the middle ages, and indeed battlefield weapons became much more varied in early modern era. Although there might have been less standardization in armaments (soldiers buying the elaborate weapons you mentioned were those in the class responsible for arming themselves autonomously) you really don't start seeing complex combined-arms tactics until the early modern era, when the pike-and-shot system starts to emerge along with specializations within cavalry as well as all-important artillery.

This is reflected in primary sources: in pre-gunpowder Italian warfare, documents refer simply to "Pedoni" or "Fanti" both meaning "those on foot." Because almost all infantry was armed with spears, there was no need for distinction. You do sometimes see texts specifying "Balestrieri," meaning soldiers armed with crossbows, but the crossbow was more of a supplementary weapon typically used by the middle class; as the enemy closed in a crossbow could be easily set aside and swapped for a spear.

The only serious distinction is made between infantry and cavalry, with extensive thought going into the best proportion of infantry to cavalry in military thought at the tame. This is because by and large, pre-gunpowder military tactics in Europe involved a static center of spear-armed infantry and the more mobile cavalry on the wings. You do see some unique cases of combined arms, as with English archers who could also engage with side-arms as the enemy closed in, although they aren't exactly medieval (or if they are, only existed at the very tail end of the middle ages). In other parts of Europe you also see crossbows, especially in armies raised in more urbanized regions (Burgundy and the aforementioned Italy come to mind). But because the crossbow was a middle-class weapon, when on the field of battle those using them could be expected have an attendant bring them a spear when they fell back into the rank and file as the enemy drew close, or even mount a horse and join the cavalry.

So although individuals might have slightly different-looking weapons, we can say that historically soldiery only needed to be differentiated based on the method of engagement: on foot, at range, or on a mount.