19th century British Army & East India Army

I'm trying to sort the naming conventions for the British Army and
the East India Army c.1850.

squealing...

A very broad question.
should get you started ... lots of info around the different structures.
Just remember that it went through four distinct phases ;
the moguls, before the mutiny, after the mutiny, and after independence
.....

- Was the British Army of the 19th century colloquially known as the
"British Army" but legally or properly known as something else, e.g.,
"The Landed Forces of ..." or similar?

- Was the East India Army a separate legal entity from the British
Army? Similar to the question above, was it known colloquially as
the "Indian Army" but legally coined as something else? The British
Library's web page, given below, cites the "Indian Army" (as well as
the Indian Medical Service and the Royal Indian Navy), so this would
seem to be the appropriate, contemporary term.

I'm also trying to sort the organizational structure of the 19th
century county Militias vis-à-vis the British Army. For example,

squealing...

Again, the above site should get you started.
Sometime the navigation is a bit clumsy, it can be better to search the
site from web-search, e.g. entering
will find all pages containing the term militia from the site.

were the English county militia part of the British Army? Similarly,
were the Irish county militia also part of the British Army? The web
site, cited below, seems to indicate that the county Militias were
part of the British Army structure:

Thank you for any pointers offered.

Cheers,
Alison Kilpatrick
Annapolis Valley, Nova Scotia