I don't think so. Even if it's said in somewhat similar kind of fashion to tell one is stronger/equal to other, I think they were having a relation similar to that of Smoker and Luffy.
Sometimes, Smoker had the chance to kill/attack Luffy but because of some Humanity reasons, he didn't and gave him another chance.
Similarly, Luffy has nothing to do with Smoker but saved him whenever Smoker was in a pinch of death.
Both the parties know each others' motives.
Like Roger knew that Garp is doing this for civilians' safety and is not a complete puppet of World Government who does anything ordered. Garp thinks by himself and decides what he must do at that moment.
Similarly Garp fights with Roger, But due to some reasons he leaves Roger free. Maybe because of Roger's personality which is difficult to find in pirates.
Sometimes, Smoker had the chance to kill/attack Luffy but because of some Humanity reasons, he didn't and gave him another chance.
Similarly, Luffy has nothing to do with Smoker but saved him whenever Smoker was in a pinch of death.
Both the parties know each others' motives.
Like Roger knew that Garp is doing this for civilians' safety and is not a complete puppet of World Government who does anything ordered. Garp thinks by himself and decides what he must do at that moment.
Similarly Garp fights with Roger, But due to some reasons he leaves Roger free. Maybe because of Roger's personality which is difficult to find in pirates.