It is more accurate to say that the majority of bushi, except for upper-class bushi, formed a part of the samurai status, rather than that the bushi who were recognized as those who served the aristocrats were called samurai, as they say.
よく言われるように貴族に仕える存在として認識された武士を侍と呼んだと言うよりもむしろ、上層武士を除く大多数の武士が侍身分の一角を形成したと言った方が正確であろう。