What is the difference between a "statistician", "applied statistician", and an academic applying advanced stats within their field? Within academia, I am wondering how statisticians use the titles/description of "statistician" versus "applied statistician."  Also, what is the difference between an "applied statistician" and an academic researcher whose work focuses on or involves the application of (relatively) advanced stats to questions in their field (I'll call this a Quantitative ________, where the blank can be any field).  What types of training and expertise do these different titles/terms imply?  

Context: I am a PhD biologist and am applying for a lectureship in a stats department and am not sure how my definition of these terms/roles compares to those of actual statisticians.  To my peers I refer to myself a "quantitative ecologist." I am wondering if I can call myself an "applied statistician" or if that would be overreach given my training (I have taken a number of applied stats courses but am mostly a self-taught user of stats and programmer).

In my mind


Academic statistician: PhD in stats, math, or biostats and highly trained in fundamental mathematics and theory of stats.  Might work on theory, methods development, or directly on applied questions.  Key diagnostic: can convey statistical ideas entirely in matrix algebra.  EDIT:Publishes all their work in statistics journals.
Applied statistician: PhD in any academic field, whose research/work is focused on development and/or application of novel or highly advanced methods to applied problems.  Might or might not have high levels of formal training in math and stats but is fluent in mathematics.  Key diagnostics:   EDIT:Publishes most or all of their work in statistics journals.
Quantitative _______: Similar to applied statistician, but whose training in math might be less complete or formal, and/or might focus more on computational aspects of statistical application than mathematical aspects (Such as development of computational algorithms, statistical packages, best practices, etc).  Key diagnostics: is fluent in a programming language and/or teaches their department's grad-level applied stats class.EDIT:Publishes their work in journals within their field.
It is always interesting to me to see how different people outside of statistics perceive it. (I am a Ph.D. in statistics who had worked in academia, international organizations, and industry.)

In American academia (I am not qualified to speak for other countries), whenever you see somebody with the title that has "statistician" in it, it probably means they run SAS PROC POWER for somebody in medical school or in agriculture (grant land universities with outreach programs). This is a lowly job, for the most part, and you rarely if ever publish: more often than not, you are an acknowledgement on a paper, not a co-author. Biostatisticians though can often advance themselves to co-authors and co-PIs when a grant/project requires a statistician to be written in as a senior staff member of the team for quality control purposes.

I would have a somewhat difficult time imagining a stat department in a research school looking at somebody whose degree is not in statistics nor mathematics for a tenure-track position. The teaching positions can be filled with the department's own grad students or recent graduates who could not find an academic job. I heard that in some universities (California state system), hiring somebody to teach statistics courses runs into an odd difficulty: statistics is taught at math departments, but math departments are only allowed to hire graduates with a degree in mathematics.

So your hopes shouldn't be very high, and if you are hired into a stat department, you probably won't be given any courses above the first couple of undergraduate intro courses -- t-statistics, ANOVA, regression. A 3+3 load would also leave no time for any work back in biology for you.

Having said all that, I think it would be fair if you were to call yourself "an applied statistician" in your letter. I had called myself a "quantitative methodologist" when applying to quant psych jobs (to no avail).

Your classification is a bit silly, BTW. There are branches of statistics, Bayesian methods or rank methods for instance, that do not think in terms of matrix algebra at all. And, with few exceptions, econometricians or reliability engineers don't have any reasons to call themselves applied statisticians, as it does not give them any promotions or any additional funding. And even if they did, "proper" statisticians (those with PhDs in statistics) may not agree with this denomination (even though a good econometrician knows asymptotic theory of statistics way better than an average Ph.D. in statistics these days).