All people in the Army are soldiers, all privates are soldiers, but not all soldiers are privates. Some are officers who are commissioned, but some are officers who are not commissioned. Obviously if every private was called private it would be confusing, so some privates are called things like trooper, driver, gunner, craftsmen (even some women are called craftsmen), sapper or signaler. Not all the drivers actually drive because some of them cook, but we don't call them cooks, for that matter, not all drivers are called drivers - some of them are privates or gunners. Gunners as I’m sure you know are the guys that fire guns, unless of course they are drivers or signalers in which case we call them gunners rather than drivers or signalers just to make it clear. All gunners belong to the artillery, except that in the infantry we have gunners who are called privates because they fire a different sort of gun, for the same reason we call our drivers and signalers private as well.
A Lance Corporal is called Corporal, unless he is a Lance Bombardier then we call him Bombardier to distinguish him from full Bombardier, who is just like a Corporal. All other ranks are called by their rank for the sake of simplicity except that Staff Sergeants are called Staff, but they are not on the staff, some Warrant Officers, who are not officers, are called Sergeant Major although they are not Sergeants or Majors. Some Warrant Officers are called Mister which is the same thing that we call some officers but they are not Warrant Officers. A Lieutenant is called Mister because he is a subaltern, but we always write his rank as Lieutenant, and Second Lieutenant, and of course second comes before first.
When we talk about groups of soldiers there obviously has to be clear distinction. We call them Officers and Soldiers although we know that officers are soldiers too. Sometimes we talk about officers and other ranks which is the same as calling them soldiers. I guess it is easiest when we talk about rank and file which is all the troops on parade except the officers and some of the NCO’s - and a few privates - and the term is used whether everyone is on parade or not. A large unit is called a battalion, unless its a regiment but sometimes a regiment is much bigger than a battalion and then it has nothing to do with the other sort of regiment. Subunits are called companies unless they are squadrons or troops or batteries for that matter. That is not radio batteries and don't confuse this type of troop with the type who are soldiers but not officers.
Mostly the Army is divided into Corps as well as units, not the sort of corps which is a couple of divisions, but the sort which tells you straight away what trade each man or woman performs, whether he is a tradesman or not. The infantrymen, for example, and the Artillery Corps has all the gunners. Both of these Corps also have signalers and drivers except those who are in the Signals or Transport Corp. Both of these Corps provide special service and thats why the Transport Corp provides cooks. In fact the Signals Corps is not a service at all because it is an Arm. Arms do all the fighting, although Signals don’t have to fight too much, rather like Engineers who are also an Arm but they don’t fight too much either.
So you see, it’s really quite simple.