Repeats vs Replications I've seen e.g. the minitab explanation on this topic which isn't bad but though, in the end, I can't explain which statistical term or the like I would (or could) investigate with each of them.
I understood it is variability but is the variability from a replication simply greater than from repeating or is it a "different" variability?
Does it make sense to investigate both?

I don't find the "replicate" versus "repeat" terminology to be very helpful, and it seems to conflict with common use of the word "replicate" in phrases like "technical replicate." As I understand the Minitab explanation:

repeat measurements are taken during the same experimental run or consecutive runs, while replicate measurements are taken during identical but different experimental runs, which are often randomized.

what they call "repeat measurements" seems to be what many would call "technical replicates."
Rather than getting hung up on terminology, think instead about the various sources of variability among a set of measurements.
One source of variability is in the measurement system itself. That's what primarily shows up in what Minitab calls "repeats" or others call "technical replicates." For example, multiple measurements of a chemical in a single sample can give different values.
That's of great importance if you are trying to design a better measurement system, but it can be of secondary importance if you just want to use a measurement system to study some phenomenon of interest. If the measurement system has a lot of inherent variability, you might take multiple measurements on each sample to deal with that problem. Multiple measurements from the same sample aren't independent of each other, however, so you need to take that into account in the analysis.
The other source of variability comes from sampling from a population. For example, if you want to know how a drug affects levels of a metabolite in the blood, you might take several measurements on each blood sample. The variability of main interest, however, comes from the differences among individuals who received the same drug. Many would call those samples from different individuals "biological replicates"; Mintab seems to call them "replicates" without additional qualification.
