(I'm only discussing ranks used in the US Air Force, because that's where my experience is...)

The basic unit of the post-classical army was the company, The start of commissioned officer rags was the captain, in command of the company. Captain is a word that means "head man" or chief, derived from the Late Latin word captions.

Then, assisting the captain with command of the company was the lieutenant. Lieutenant was derived from the French language; the lieu meaning "place" as in a position; and tenant meaning "holding" as in "holding a position"; thus a lieutenant is somebody who holds a position in the absence of, or "in lieu of," his superior.

Usually serving at the company level, one captain was granted general (overall) authority over the field armies by the king, and was called the captain general. The lieutenants of tthe captain general were designated lieutenant generals to distinguish them from lieutenants subordinate to mere captains. The sergeant acting as staff officer to the captain general was known as the sergeant major general. This was eventually shortened to major general, while captain general was shortened to simply general.

Around the end of the 16th century, companies were grouped into regiments, or columns. The officers commissioned to lead these regiments were called colonels (column officers). The lieutenants of the colonel were (naturally) the lieutenant colonels. In the 17th century, the sergeant of the colonel was the sergeant major. These were field officers, third in command of their regiments (after their colonels and lieutenant colonels), with a role similar to the older, army-level sergeants major (although obviously on a smaller scale). The older position became known as sergeant major general to distinguish it. Over time, the sergeant was dropped from both titles since both ranks were used for commissioned officers. This gave rise to the modern ranks of major and major general. Thus, majors outrank lieutenants, but lieutenant generals outrank major generals.

Regiments were later split into battalions with a lieutenant colonel as commanding officer and a major as an executive officer. Brigades, invented in the 15th century by the British as the smallest Independent tactical unit, are composed of two or more regiments or battalions, and are headed by brigadier generals.

Finally, sergeant is from the Latin serviens, 'one who serves', through the French term sergent. The term sergeant refers to a non-commissioned officer placed above the rank of an airman and immediately below a lieutenant (the first rank of commissioned officers). Airman, in turn, was selected by the chief of staff of the US Air Force shortly after it was founded in 1947, to distinguish junior enlisted members from soldiers, sailors, or Marines.

That's it — thank you for reading!