What is the relation between measures, constructs and concepts? It is uncontroversial to say that the cognitive sciences do not exclusively deal with directly observable phenomena, but nonetheless aim to study the physical causes of behavior and cognition scientifically. &quot;Grasping&quot;, for instance, is directly observable, but cognitive science also studies &quot;intelligence,&quot; which is not directly observable, at least not for all conceptualizations of intelligence.
When cognitive science studies such an unobserved quantity, the difference between the general concept, the unobserved construct, and the direct measure is sometimes rendered implicit. More colloquially: go far enough down the methodological rabbit hole for an unobserved construct, and you will likely eventually find a patient zero paper that defines a broad folk concept, then makes a spherical-cow or just-so statement that a construct maps on to the concept.
Example: Working memory
For an illustration of a just-so definition, take Baddeley and Hitch's definition of working memory in their seminal 1974 work as a replacement for the classical short-term/long-term memory model:

a system that provides temporary storage and manipulation of information

(The relationship rendered implicit here is [&quot;memory&quot; -&gt; STM/LTM -&gt; WM/LTM].)
To be fair to Baddeley &amp; Hitch, and so as not to single them out, Baddeley has later defended this problem with their model on productivity and guide to discovery grounds (Baddeley, 2007). I find this quite reasonable, and I do not mean to impugn their excellent research or the model's productivity in any way, only to use the example as an illustration for the question.
Problem of implicit relations
Implicit relations are antithetical to the practice of science because they engender unstated assumptions and hidden theoretical incompatibilities. It is also antithetical to science communication and scientific literacy, because important words like &quot;intelligence&quot; and &quot;memory&quot; become effectively polyvalent, with subtly different meanings that are not apparent without considerable study. The relationship between IQ and intelligence is the prototypical example.
Question
What is the relation between measures, constructs and concepts as actually used in the cognitive sciences? (Contrast intelligence or memory with grasping or walking, if concrete examples are helpful.)
Please read my comments to the question and current answer before asking for additional information.
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References

Baddeley, A. (2007). Working memory, thought, and action. Oxford University Press.
Baddeley, A. D., &amp; Hitch, G. (1974). Working memory. Psychology of learning and motivation, 8, 47-89.
In speaking to constructs vs. measures, I believe that the difference is clear and implied in your background: constructs are that which cannot be directly measured (but we assume exists), where measures are directly measurable attributes that we assume relate to the construct. The process you seem to be questioning is that of the operational definition, or the process of defining that which cannot be measured (the construct) as that which can (the measurement). Your concern that these are not equivalent is quite right, and many papers are written for the sole purpose of explaining why a certain measure matches a theoretical construct (the process of measurement validation and establishing construct validity).

As to why operational definitions are necessary, the straightforward answer is simple: communication. As constructs are not measurable (in many cases), some type of operationalization must be used. If multiple claims are made on a construct, each using different operational definitions, the results may be contradictory purely due to the differences in the operational definitions assigned by separate researchers! (Education Letter, 2013)

Using operational definitions instead of simply listing the construct can help researchers better determine which results should be comparable. Remember, each of these definitions may have been validated, yet differences in the measurement will naturally yield differences in the data that may not be relevant to the construct. This is the heart of construct invalidity (Groves et al., 2009).

I've always enjoyed seminal papers, and one that you may be interested in is the seminal work defining construct validity (and distinguishing it from other types) by Lee Cronbach and Paul Meehl.

"Construct validity is ordinarily studied when the tester has no definite criterion measure of the quality with which he is concerned, and must use indirect measures. Here the trait or quality underlying the test is of central importance, rather than either the test behavior or the scores on the criteria" (Cronbach &amp; Meehl, 1955, p. 282). 

It sounds like you may take issue with failure to apply correct validity checks, and the application of the correct types of validity to the correct situations.

I hope this help to clarify the nuances of a very involved question! Perhaps the heart of the question/solution is this: though constructs and operational definitions of constructs get used interchangeably, they shouldn't be.

References

Cronbach, L. J., &amp; Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281–302.

Groves, R. M., Fowler, F. J., Jr., Couper, M. P., Lepkowski, J. M., Singer, E., &amp; Tourangeau, R. (2009). Survey Methodology (Vol. 2). John Wiley &amp; Sons.

General science; new findings reported from Carnegie Mellon University describe advances in general science. (2013). Education Letter, 90.