RQ2 had Battle Magic and Rune Magic.
RQ3 had Spirit Magic, Divine Magic and Sorcery.
RQM1 had Rune Magic, Divine Magic and Sorcery.
RQM2 had Common Magic, Divine Magic, Sorcery and Spirit Magic.
Legend has Common Magic, Divine Magic, Sorcery and Spirit Magic.
The terms in order are basically the same, So, RQ2 Battle Magic, RQ3 Spirit Magic, RQM Rune Magic and Legend Common Magic are very similar, but RQ2 Rune Magic and RQM Rune Magic are very different, as are RQ3 Spirit Magic and Legend Spirit Magic.
The name "RuneQuest" really had nothing to do with the game. Very few people used runes, and there were no rules for runes, and very few people went on quests, RQ was mostly about adventuring. But, it's a good name.
In RQ2, Rune Priests gained the Magic Rune, Rune Lords gained the Mastery Rune and members of cults gained an association with their cult's runes. However, this had little impact on the game itself.
Mongoose tried its very best to use Runes in the game, but their implementation was troubled and didn't really work with any setting. RQM2 pulled runes completely and Common Magic did not rely on the use of runes, something that Legend uses.
If you want to use Runes and Quest in the game, then you could make the obtaining of runes part of the game itself.
One way of doing it would be: These runes could have a skill associated with them (e.g. Death Rune 70%, Fertility Rune 20%), based on POW+something, and a Magnitude, representing the strength of the rune, so you could have Death Rune (3) 70%. The Runes could be used to strengthen spells based on that rune, so the Death Rune could increase the strength of a Bladesharp or Disruption spell, so Death (3) 70% would increase Bladesharp 4 to Bladesharp 7, if the Death Rune skill is rolled, with standard rules for spending the extra Magic Points. You could also use the Runes themselves to gain minor runic effects, or to boost certain skills.