Spontaneous musical creation in real time is known as

composition, texture, improvisation, or dynamics

The closest thing that I can say among all of these answers would be improvisation. The definition of improvising is adapting to the situation in a better manner appropriately. So let's say when a musician is already on stage and makes a mistake while playing the guitar, he has to improvise a bit so that his mistake will not look like one. He is spontaneously creating something while he is on the spot. In a sense, he is improvising his original work and making something somewhat different.