Neither impression was great, but your surface readings of the two series were even worse. Backwards, even.
The number of original series episodes where they actually explored planets "for the hell of it" are a small minority. Far more started with i) rescue missions, ii) responding to distress signals, iii) diplomatic missions, or iv) transporting medical supplies. Moreover, there was no threat of galactic war in TOS because forced the Federation and the Klingons to play nice [https://en.wikipedia.org/wiki/Errand_of_Mercy].
Meanwhile, on TNG, the Federation regularly had to contend with powers that were roughly equal to them: the Klingons, the Romulans, the Cardassians and the Ferengi. The last time the Federation went to war with one of these, it was a bloody mess they were still cleaning up at the end of Deep Space Nine! So of course the Federation always tried the diplomatic option first! Is it a coincidence that the a foe immune to diplomacy [https://en.wikipedia.org/wiki/The_Best_of_Both_Worlds_%28Star_Trek:_The_Next_Generation%29]?
/nerdrant