Laserstorm plays very simple but the rules throw a LOT of terms at the player.
So we're going to clear up what each level of the organizational hierarchy mean:
One figure or base with troops on it, representing one individual vehicle or a fireteam of 4-6 soldiers.
This is the smallest element that can exist in the game and is basically one figure.
Several stands are organized into Units. A unit must stick near each other during the game and will take morale checks together.
This is what Epic used to call a "detachment" back in Space Marine days.
A unit consists of typically 2-6 stands but some stands can form a unit all on their own.
The Task Force is only used as an organizational step. If you build your own army using the included rules, you build a number of Task Forces.
Each type of Task Force will dictate how many units of each type you can include.
Players of warhammer 40K will recognize this as very similar to the detachment organizations in later versions of that game.
A task force typically has 3-6 units comprising it.
On the table, your force is always broken into 3 individual forces for activation purposes. Each such battle group receives one card in your turn deck.
Battle groups usually contain multiple units. In a large battle, each battle group may contain a task force or the task forces may be broken up into multiple battle groups.
A battle group may contain anything from 2 to 20+ units. It may contain entire task forces or parts of them.
All your forces in one game is an Army. During a campaign, each separate force on the campaign map is an Army.
Armies consist of one or more task forces.
When an Army takes the field, it is temporarily assigned into 3 battle groups.
An army thus always contains at least 1 task force and could potentially include any number.
On the tabletop, an army always forms into 3 battle groups.
Just like a tabletop army is broken into 3 battle groups for activation card purposes, so our campaign army is broken into 3 army groups.
An army group will have at least 1 army and may have many more, depending on the size of the campaign.
The entire, combined forces available to a player in a campaign makes up their Expeditionary Force.
The EF always consists of 3 army groups and may thus contain a very large number of armies.
Hope that helps!