However, the Queen is Commander-in-Chief of the Army and holds the rank of Field Marshal.If you're talking about the British, there's no such thing as "the Royal Army". There are a variety of Royal regiments and Corps, but the army as a whole answers to Parliament, not the Crown.
She is C-in-C of the Royal Navy and RAF too holding the rank of Lord High Admiral and Marshal of the RAF. However, like the Army they are really controlled by Parliament.
There isn't a Royal Army because as you wrote its a collection of corps and regiments while the RAF, Royal Navy and Royal Marines are single bodies. As you also wrote many of them have the honorific title Royal (like the Royal Regiment of Artillery and the Corps of Royal Engineers), but some, usually infantry regiments, don't