So, first I'll unpack a few things. What I will be talking about is mainly focused on the French Imperial Army, I don't know enough of the other army compositions to help but I am sure that we have the right people to help. Second, within the French army, there is a difference between light infantry and skirmishers and I'll go into that in a bit.

So, what makes light infantry? Generally light infantry was made of men between five feet and five four to five six. They were chosen for being nimble and intelligent, being able to conduct open order formations without getting confused (clearly they didn't think much of soldiers intellect). So light infantry (or chasseurs a pied) would be trained to fight in both a line formation and open order formation. From there, what they would do would vary from what was needed but more often than naught, they would fight in line formation.

Now, the real use of light infantry was to establish a foothold; ideally a French commander would send his light forward to make contact with the enemy and hold them there. From here, the regular line would march up and fight the now tired enemy while the light pulls back for a flanking attempt. So, the use of light is meant to stop the enemy and buy time to pull in more forces to defeat the enemy.

now, for skirmishing. As I mentioned, yes the light was trained in open order combat. They could skirmish if needed but often they would leave it to the voltigeurs, an elite company of sharp shooters. Before 1809, a French Line battalion would consist of did companies of about 120 men, one company of elite Grenadier (whom are the tallest and most skilled of the battalion), and a company of elite sharp shooters (the aforementioned voltigeurs). A light battalion would have the same composition, having chasseurs instead of standard line and carabiners instead of grenadiers. The voltigeurs would be the ones skirmishing until they would give way for the standard light infantry in line formation

There are specific skirmishing battalions, trailleurs, which would often be either elite infantry like the Trailleurs De la Jeune Garde but those are unique units.