Well are you going for a day hike or are you going for a trail run? If you`re going for a hike I would wear running clothes just because you think you`ll be faster. If your going on a hike then enjoy yourself enjoy where you`re at, instead of speed walking through the woods, slow down and take notice of the things you`ve ran by before. With that said then you wouldnt need running clothes. Wear clothes that are comfortable and practical. I`d still wear synthetics in case you get caught in some rain, perhaps the convertible pants(legs zip off to shorts). And always carry the 10 essentials, we never plan on being stuck out in the woods overnight but thats why its called an accident. Its better to be prepared for it than not.
Now if you are going for a trail run then yes I would just wear running clothing and still take a small pack with the 10 essentials in them. When trail running I fit everything into my camelback pack, so it includes my water and the 10 essentials