From the 1860 perspective the number of companies in either a Battalion or a Regiment was fairly fluid.

For example in the manuals the terms "battalion" and "Regiment" are used fairly interchangablely. However, as a matter of practise a battalion consisted of any formation which was 7 companies or less. A regiment was a formation of 8 to 12 companies. Companies designation ran from A to M (omitting the letter "J" because it was too easily confused with the letter "I" in written correspondance, orders and communications) Many early battalions were either increased or combined to make regimental strength Units.

The concept of the usage of a battalion was as lightly equiped, fast, manuverable troops. Not encumbered with a lot of baggage such as command structure with ordance and supply and simular "normal" operations of a larger unit. Therefore they could be used to scout, or as pickets, or skirmishers, or to guard the flanks of larger formations. This is where I believe the concept of "light Infantry" comes from. It had nothing to do with what equipement the individual soldiers carried.

The number of companies in a regiment also depended on whether the Unit was a "regular army" unit, or a "volunteer" Regiment. Units of the regular Union service, such as the 1st US Infantry, contained 3 battalions of 5 companies, much as the modern day formations. The idea here was flexibility in the usage of the troops. Confederates did not use this style of organization and stayed with the 10 company regiments for the regular units like the 3rd Confederate Infantry.