Update
After doing a little digging, I had this distinction offered to me:
You might translate "substanzwissenschaftler" to empirical scientist or empirical researcher. Generally, the empirical scientist relies primarily on observations of nature and comes to conclusions that might be used to infer the properties of nature in broader terms. (This is the scientific method.)
A theoretical scientist, on the other hand (including mathematicians), might postulate fundamental properties (which may have been obtained from an empirical scientist) and then predict how nature (and you can include mathematics in this) might behave in broader or more general ways. Theoretical science can also be refered to as pure science.
Then there is the applied scientist, who would try to validate the theoretician's predictions using experiments designed for that purpose.
Contrary to common opinion, sciences like chemistry, biology, and physics, are not simply empirical sciences, and there are many scientists that take on roles in the theoretical and applied science for those disciplines.
Likewise, math is not strictly a pure or theoretical science. Statistics is a form of applied mathematics, where the goal is to use mathematics as a tool to study natural phenomena, rather than to extend the theory of mathematics. Cryptography is a case of applied math that relies heavily on derivations from theoretical math.
Update 2
Gerhard Schurz complicates this somewhat in his paper A Llgemeine Wissenschaftstheorie (A general understanding of science). He wrote the following (with a purposeful reordering of his points by me):
Thus one can classify Substanzwissenschaften as
1) Empirical sciences - all of which refer to empirical data of any kind, that is also for example: historical sciences (historical sources), literary sciences (texts), etc.
2) Experimental sciences - those which do not only have empirical observation data, but rather those in the form of controlled experiments. We come to the significance of the experiment against free "field observation" in the back of chapter 3. This category excludes many "spiritual sciences", such as history sciences, literary sciences, macro-sociology, etc., because one can not experiment here. This includes, for example, experimental psychology, and, of course, the classical natural sciences.
3) "Dissecting" sciences - these are the ones who not only observe their empirical objects or do experiments with them, but also physically decompose them into small parts, or even reverse from them - the "classical" natural sciences such as physics, chemistry, in vitro biology
4) "Speculative" disciplines (non-empirical but synthetic, non-scientific in our sense)
From the first two points, I would imagine Schurz's definition of Substanzwissenschaften is applicable to both empirical and applied scientists. The third point seems to describe what an opportunistic applied scientist might do. Therefore, I think you might prefer applied scientist over empirical scientist, but that might be a matter of personal taste.
The fourth point by Schurz puzzles me a little. It describes what is known as jumping to conclusions, meaning drawing conclusions without the intermediate supporting logic and evidence. (See how Kant compares synthetic to analytic here.) I might put this in the hacking category, myself and I suppose someone might have an argument with Shurz about this one, since it seems to undermine some of the more sacrosanct principles of science, as I understand them.
(I'll leave my earlier answer here for reference, since you thought the figure was helpful for updating your question.)
It might help to pull the word apart and play with it a little. By looking for the words "substantive science", I came up with this chart, along with some of the descriptions for it:
It's what my former data analysis prof called domain knowledge. It's knowledge related to specific facts, to relationships about certain subject matter, not just a technical process. Hacking skills could be the ability to cleverly draw up code from scratch to solve problems; math and statistics would allow you to just do math and stats to data; but substantive expertise would let you use your background in biology to apply those things to finding diseases in DNA codes. If you don't have substantive expertise, you usually don't even know what to do with your technical skills that matters, even if you do have any technical skills. (from Quora - What is substantive expertise in data science?)
Themes common term I've seen for this is subject-matter expert. You might also use domain expert.
There is a good description of this in wikipedia:
A subject-matter expert (SME) or domain expert is a person who is an authority in a particular area or topic. The term domain expert is frequently used in expert systems software development, and there the term always refers to the domain other than the software domain. A domain expert is a person with special knowledge or skills in a particular area of endeavor.
