As far back as the original game goes, a starting fighter was a veteran with all that this implies. He/she has been battle tested and seen action. Every level thereafter added to this capability over the ordinary man. A 4th level fighter was a hero because he/she could fight with the power of 4 ordinary men alone.
The 1e DMG has some rules under Mercenary Soldier in the Hireling section.
* A Captain is a 5th-8th level fighter (40% are 5th level, 30% 6th, 20% 7th, and 10% 8th) - they control up to a score of soldiers per level + one lieutenant per level (excluding the needed serjeants)
* A Lieutenant is a 2nd-3rd level fighter (70% 2nd level, 30% 3rd level) - they control up to 10 soldiers per level (adding to the total led by the captain, and excluding the needed serjeants) and have one extra serjeant per level beyond that that don't directly command troops
* A Serjeant is a 1st level fighter- they can control up to 10 soldiers each (sometimes as few as five)
* A standard soldier is a 0-level man-at-arms.
That means an "average" mercenary company at full strength (e.g. with every commander maxing out their command skills) has around:
1 - 6th level Fighter (Captain)
2 - 3rd level Fighters (Lieutenants)
4 - 2nd level Fighters (Lieutenants)
40 - 1st level Fighters (Serjeants)
260 - 0-level Men-at-Arms
How different should a first level fighter be from a common soldier?
Preferably, very different. Soldiers and mercenaries know how to use weapons. Fighters are consummate athletes and masters of the martial arts.
How different should a first level fighter be from a common soldier?
Fighters are often described as better than infantry, your rank-and-file soldiers.
This was true in 3e (which had the warrior NPC class) and 4e (which used different rules for NPCs giving PCs an edge). But in 1e and 2e, NPC soldiers were either fighters or level 0 commoners (and thus mechanically equal to the pig farmer).
How different should a first level fighter be from a common soldier?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.