Best resource for lances are Alpha Strike something.... uh, well, the book that includes force building, and/or Campaign Operations.
They list lance types and what are required for them, and more or less answer what they're for.
But on top of my head...
Heavy, light, or whatever other weight-related adjective more or less tells the average weight of the lance.
-Command Lance is usually additional to lance. So you might have a company and a Command lance, or battalion and Command Lance (in larger formations the Command Lances form a Command Company as i understand it).
Naturally dedicated to body guarding the commander but may also include additional capabilities, act as a reserve.
-Battle lance is your mainline combatants, focusing on armor and firepower over speed. When combined with weight class, it may drop "Battle", ie "Heavy Lance" most likely means "Heavy Battle Lance".
-Striker Lance, also known as Cavalry Lance, contain Above average speed 'Mechs for fast attacks or flanking attacks.
-Recon/Scout Lances are for scouting, duh. Lighter and faster 'Mechs are the norm.
-Fire Lance means fire support lance. Contains long-range support 'Mechs like Catapults, Archers, JagerMechs, etc.
-Pursuit Lance is one i've never quite figured out. Usually it contains fast 'Mechs with reasonable firepower, so they're rather similar to Striker Lances but occasionally also Recon Lances.
What others there were...