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This answer to How does an onboard atomic clock help interplanetary navigation? says:

Range-Rate is the two-way measurement of signals broadcast from one location on Earth, received and retransmitted by the spacecraft in a frequency-coherent way and received back on Earth. It's also called delay-Doppler. You get a range from the delay, and a rate-of-change of range (a 1 dimensional velocity) from the Doppler shift.

and a comment below it calls out my reference to delay-Doppler as another name for range-rate.

I had always thought that the expression "range-rate" refers to measurements of both the range (via delay) and the rate of change of range (via Doppler).

Granted delay-doppler is usually used on objects with passive reflection, like in measurements of Venus or Mercury or a near-Earth asteroid from Earth, whereas in space the delay-Doppler measurements are made possible by coherent transponders on spacecraft as the are way to small and too distant to be measurable by passive radar.

Am I mixing up things that are in some way fundamentally different or are they essentially the same idea but differ only in their practicalities?

Question: What are the differences (if any) between the techniques of range-rate and delay-doppler measurements?

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It's mostly a terminology question and an application question. As you've correctly pointed out, "delay-Doppler" is the term used for radar tracking of uncooperative systems. For cooperative spacecraft tracking, the term "Doppler" measurement or "range rate" is used. The underlying physical principals are the same.

The spacecraft will receive the ranging signal and (at a minimum) amplify it and return it, thereby greatly increasing the signal-to-noise ratio compared to radar tracking.

Volume 1 of the JPL DESCANO Book Series, Radiometric tracking techniques for deep space navigation, explains how range measurements and Doppler measurements are computed (cf. screenshot below).

enter image description here

I think it's also important to note that, in orbit determination, ground stations may provide a number of different kinds of measurements, not just ranging and range-rate. A common approach is to provide angle measurements and Doppler. An exhaustive list of useful measurements for tracking can be found in the CCSDS Tracking Data Messages blue book (PDF), table 3.5 on page 3-25 (PDF page 43).

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    $\begingroup$ I've just realized something else; when I see "range rate" I have always associated "range" with "delay" and "rate" with "Doppler", and that wasn't right. "Range rate" is one term, more or less the rate of change of range. Radar's "delay" is associated with "range", so "Delay-doppler" should be "range and range rate". Delay-doppler also expands out into the big world of radar imaging of poorly (or un-)resolved but rotating bodies when they're observed for long enough and the reflection data is modeled correctly) $\endgroup$
    – uhoh
    Oct 3 '21 at 23:33

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