There is no “same” rainbow for everyone. Each observer has their own rainbow. Nor is the rainbow you see necessarily located at a specific distance from you. Some of the refracting droplets may be yards away, some miles away, but they all contribute to build “your” rainbow.
It’s a matter of angle, not distance. If the sun is unobstructed, low to the horizon and at your back, and if there is some mist-producing phenomenon somewhere out in front of you (whether it be a weather system or a waterfall or a sprinkler), you stand a good chance of seeing a rainbow provided that you are directly in the line between the sun and the mist. If you were a little out of line, the rainbow would disappear.
So whether someone at a distance would also be seeing a rainbow at the same time as you would depend entirely on how big the mist-producing phenomenon is. A rainstorm is big, so someone far to your right or left could still be in a direct line between the sun and the storm.