I've made a new 4 day full body routine. What I'm wondering is wether I should do multiple types of training for one muscle. For example, is it enough for my chest muscles if I only do push-ups? And is it enough for my triceps to only do standing tricep extensions?
It depends on your fitness level.
You have to progressively overload your muscles for any sort of gain, weather its fitness orientated or aesthetically orientated workout.
For an individual with a high level of fitness, one workout per muscle is not enough.
However, for a beginner or intermediate it could be enough because many muscles work in correlation to each other and are either antagonists of each other or synergist.
For instance, the above example, push ups also workout your triceps. So your triceps are being worked out on two exercises. In one it is the prime mover, in the other its a synergist together with the your chest muslce, (pectoralis major)