Slitherine

One thing i do not understand is why in the lists these do not coexist.

In some list where there are heavy knights, 'lesser equiped knights' are graded cav but not armoured knights.

Not entirely true, if you include possible allied contingents. Knights are graded as heavily armored when the average level of armor for a knight of that culture is fully armored rider on a caprisoned horse. Other, lesser equipped men would be included in the "lances" which make up the knight BGs, but would fill out the rear ranks. These lesser armed men could sometimes be detached from their lances and grouped together as a faster, more maneuverable element of the army. This greater mobility and lower armor level is best depicted as cavalry.
Some armies, notably Feudal Polish, had a lower level of protection compared to their richer neighbors, but fought in a similar style, so remain armored knights even though they may have heavily armored foreign elements, either mercenary BGs or foriegn allied contingents as part of their army.

Greg Boeser