Lets suppose a spaceship travels with v = 0.9c relative to the Earth. The time inside the spaceship would pass slower than on Earth. Would the astronauts measure a different speed (that means, a different one that the observer on Earth does) in relation to the same reference frame (Earth)?
The time inside spaceship would pass slower than Earth and distance measured by astronauts would be less than distance measured by Earth scientists. As $speed=distance/time$, they would observe different speed of something other than light. Speed of light would be observed same by all.