What is the relation between statistical and instrumental uncertainty?

I’ve been studying some error analysis on An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by John R. Taylor for an introductory course. At the beginning of chapter 4 I read that in some cases we use statical analysis to evaluate the uncertainty, in other cases we use the propagation of errors due to instrumental resolution. Suppose we use a ruler (assume negligible systematic error for now) with an instrumental resolution of, say $delta l=1mm$. The lenght of an object will be given by:
begin{equation}
lpmdelta l=lpm1mm
end{equation}
Where $l$ is our best value for the lenght. Otherwise, I read that we can make several measurements of that quantity (the book does not write the instrumental error) and then take the standard deviation $sigma_l:=delta l_{rand}$ as uncertainty of a single measurement (due to random errors). If we also have some source of systematic error $delta l_{syst}$, the total error will be given by
begin{equation}
delta l_{tot}=sqrt{delta l_{rand}^2+delta l_{syst}^2}
tag{a}end{equation}

So, as far as I understand you either use instrumental error or statical error, but in one of our classes the professor told us that if he have an instrumental error $delta l$ and a statistical error $sigma_l$ (assuming negligible systematic error), the total error will be given by:

begin{equation}
delta l_{tot}=sqrt{delta l^2+sigma_{l}^2}
tag{b}end{equation}

This equation is very different from $(a)$ because we are combining the error due to instrumental resolution (that is actually random because I might underestimate or overestimate) and the statistical error. I can’t find references to equation $(b)$ anywhere. Is it correct? Why doesn’t Taylor mention it? Can we combine instrumental and statistical error?