Do the troop classifications actually mean anything?

Every unit has a tag in it's name on the battle map in square brackets, saying what classification it is.

They run something like:
Missile
Light Infantry
Heavy Infantry
Spearman
Missile Cavalry
Light Cavalry
Heavy Cavalry
Artillery

What do they mean? Are they based on some kind of calculation of the unit's stats, or are they just an assigned value? Is there some kind of property being one type and not another carries?

Sometimes I've compared the stats of one type of infantry deemed "Light" and another deemed "heavy" and there's not a lot in it, if anything at all.

Also what is the property of their weapon type being "Light" or "Heavy" based on? Again is it something that's just assigned, or based on the properties of the weapon they use?

These are used by the AI to identify the purpose of a unit, what it is important for a) recruitement and b) deployment on the battlefield.

Placing a unit in the wrong class might have bizzarr consequences: for example a cheap missle unit classified as "light" will certainly lead to the spamming of that unit by the AI because it "thinks" - 'wow, a unit of light infantry for a bargain! Let's make a full stack of it!'

I notice as an example that the Garamantines have been reclassified from Heavy Infantry to Spearmen, that just means the AI will recruit them differently?

And will probably place them in a different way on the battlefield, yes.

Originally Posted by QuintusSertorius

I notice as an example that the Garamantines have been reclassified from Heavy Infantry to Spearmen, that just means the AI will recruit them differently?

Yes. It will/should compare their stats to the other spearmen it can raise in Lepki and will go for the better one - if possible.

Originally Posted by QuintusSertorius

I notice as an example that the Garamantines have been reclassified from Heavy Infantry to Spearmen, that just means the AI will recruit them differently?

It will recruit them differently and place them differently in formations...

But in essence for the human player, then, the classifications are largely irrelevant?

Yes

So Iberian Scutarii aren't any better at covering the flanks against cavalry than Samnite Allied Spearmen are, just because they're Spearmen and the latter are Light Infantry. Cool.

Originally Posted by QuintusSertorius

But in essence for the human player, then, the classifications are largely irrelevant?

except if you use any of the pre-made formations...

Originally Posted by QuintusSertorius

So Iberian Scutarii aren't any better at covering the flanks against cavalry than Samnite Allied Spearmen are, just because they're Spearmen and the latter are Light Infantry. Cool.

IIRC, the Samnite Allied Infantry is supposed to be classed as spearman

Originally Posted by mcantu

except if you use any of the pre-made formations...

As per the other thread, I don't.

Originally Posted by QuintusSertorius

Also what is the property of their weapon type being "Light" or "Heavy" based on? Again is it something that's just assigned, or based on the properties of the weapon they use?

This too is assigned, but AFAIK it is not used for anything but weapon upgrades.