Unit designation as well as ship classification will always remain a mystery to us enenlightenend. Also each time/ nation has its own classification. ShEm has seems to simulate WWII style armies.
In a WWII setting a division was the formation where different kind of troops (infantry, tanks) were organized, giving it a high degree of independence. Its manouver elements were mostly three regiments and it had adittional support units attached, providing logistics, communications, arty, engineers, AA, AT ...
A tank division might have 1 tank and 2 armored regiments and an airborne division three airborne regiments. A regiment would consist of several battalions of typically the same kind.
For larger scale operations divisions were organized in Corps, Armies, Army Groups and Theater Commands.
A modern brigade functions as a division with the size of a regiment. It typically has battalions as manouver elements, not regiments.
Would be nice if we could really organize our ShEm armies along these lines.