Not to quibble about definitions of what "change" means, but I thought the red shift depended entirely on the relative speed of the emitting and receiving body? A laser beam for example could not be analyzed for its red shift, unless we knew the original frequency, because there would be no spectral absorption pattern to determine the shift. So we cannot tell how far laser light traveled before it reached our sensor.
Not a quibble at all. The redshift I'm referring to is the kind of redshift due to gravity, as opposed what you're describing which is redshift due to the Doppler effect.
I'm trying to come up with a scenario to understand the difference: Say I have a triangle of emitter, receiver, and a large body, all at a fixed distance. And the receiver would see emitted light both directly and bent around the body. The bent light would be red shifted?