Good Question.

In the Civil War, Mississippi units (Infantry)...

A Regiment is a unit commanded by a full colonel, number of companies, normally ten (although some where higher or less). Although there are battalions within regiment, commanded by Lt. Colonels or Majors, the unit is identified by its regimental identification.

A Battalion (independent) is a unit commanded by a lieutenant colonel or major. An aggregation of two to ten companies (normally eight). Identified by its battalion identification.

There were varying differences in the size of staffs, i.e.

A regiment could have a

Lt. Col.
Major
Surgeon
Assistant Surgeon
Quatermaster
Commissary
Adjutant
Chaplain
Sergeant Major

A Battalion (independent) could have (but not limited to)

Major
Surgeon
Adjutant
Chaplain

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On the battlefield according to Hardees and the 4th Addition to the PIE...

A Regiment is composed of ten companies, but could be less.

A Battalion is composed of two or more companies acting together as a unit. At its initial formation, a Battalion of ten companies (e.g. a regiment) forms its companies from right to left.

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David Upton