In the beginning, there were three basic ranks:
Captain ("head") Captain just meant the boss of a military unit, without regard for the size of the unit. (Note, this meaning is why the position of commanding officer of a ship, no matter how small, is known as "captain", regardless of the rank title the individual holds.. a military band under one Captain was referred to as a "company".)
Sergeant ("servant" - the #2 who took care of details for the "head"; he was, in effect, the equivalent of the modern staff section; he also had a secondary role as a subordinate leader). Sergeants were originally officers, in what their responsibilities were.
Soldier (the more modern term "private" comes from.the medieval description of individuals who are brought into military service - whether as volunteers, levies, or conscription as "private soldiers", meaning they don't bring subordinates with them, unlike the officers).
At some point, it was decided to give the Captain a backup, who could act on his behalf when he wasn't present (as the Sergeant had his other duties to do). This was the Lieutenant ("in place of"). The lieutenant effectively displaced the sergeant as the captain's deputy, while the sergeant retained his administrative and logistics role. The Lieutenant was senior to the Sergeant, as he was the #2 in the chain of command.
About this time, the Captain had several sergeants working for him. The top Sergeant was the Sergeant Major ("big sergeant"). He was still junior to the Lieutenant.
When you collected several militaty units together, one of the captains would be the Captain General (the overall boss, over the forces in general, as captain of the entire army).
His immediate deputy was the Lieutenant General, with the same derivation (he was the "stand in" for the Captain General when necessary). As he stood above the "regular" captains in the chain of command, he was senior to them.
The Sergeant Major for the Captain General became the Sergeant Major General (the "big sergeant in general" for the whole army) He was senior to the regular captains and lieutenants in the individual units, since he was at the army level, but junior to the Lieutenant General.
Eventually, "Captain" was dropped from the Captain General, leaving him as the General. The Lieutenant General title remained the same, while "Sergeant" was dropped from the Sergeant Major General, becoming Major General (but still subordinate to the Lieutenant General who was still the #2 in the army).
Larger (but not quite "army sized") units started to be referred to as "columns", and their "captains" started being referred to "commanders of the columns", which is where the title Colonel derives from. Each column was comprised of several companies, each with their Captains, Lieutenants, and Sergeants.. The top Sergeant for the Colonel was still his Sergeant Major (and still an "officer"), and he was senior to the Captains and Lieutenants of the subordinate companies.
The Colonel obviously needed a deputy, so the Lieutenant Colonel arose, senior to every other officer in the column below the Colonel, much as the Lieutenant General was to every officer in the army below the General.
Eventually, the more senior "staff" roles and the equally important, but not as directly involved in the chain of command at higher levels diverged into different positions. The more senior, "officer type" jobs dropped the "Sergeant" part of their titles, becoming simply, Major - still senior to the Captains and Lieutenants in the subordinate companies, but subordinate to the Lieutenant Colonel (as the Major was #3 in the column chain of command). The Sergeant Major transitioned to a senior enlisted role, officially junior to the Captains and Lieutenants of the subordinate companies, but unofficially considered more senior due to his position in the column's chain of command.
Thus, the basic rank structure for senior personnel was set, with a few tweaks along the way still to come (senior officers above the Colonel in charge of multiple regiments "brigaded" together, referred to as the "General of the Brigade", or Brigadier General… Columns had changed names to "regiments", reflecting how the soldiers were drilled into regimented discipline, by the time of the introduction of brigades during the French Revolutionary period.)