[quote=@Raineh Daze]
<Snipped quote by IncredibleBee>

... this isn't a D&D campaign. By that logic, Charlemagne's paladins wouldn't be paladins, and D&D paladins may also not be paladins because of varying features. Classes aren't required to be selected from a pre-approved list of abilities equalling certain classes. >.>

<Snipped quote by Boomrocker>

Which makes the addition of a [i]fourth[/i] fighter who occupies the exact same character niche a worse overlap. 
[/quote]

In game terms, paladins are generally defined as a tanky class that relies primarily on melee combat with a touch of white magic to support their allies and boost their own longevity.
You see, historical terms are put aside for games, because it's easiest to associate names with a general set of abilities so you know what you're using. If you selected "Fighter" in an RPG, for example, and found the class wasn't very good at fighting but did have a fireball, most people would be confused or even angry.

In short, a paladin with no white magic is just a fighter.