"Logician vs Logistician" is searched far more than the letters would suggest, mostly because the nicknames sound alike. INTP and ISTJ actually differ on two letters, S versus N and J versus P, and in day-to-day behavior they are close to opposites who happen to share a quiet exterior.
ISTJ trusts what has worked and finishes it; INTP trusts what makes sense and keeps exploring it.
Two letters differ: S versus N and J versus P.
Getting both ISTJ and INTP is less common than the other pairs here, because two letters have to move. When it happens it is usually a work-versus-home split: structured and by the book at work (S and J under pressure), abstract and open-ended alone (N and P at rest). A four-scenario result shows that as two scenario types rather than one confused label.
Logician is the nickname some tests use for INTP, and Logistician for ISTJ. Despite the similar names, they differ on two of four letters.
Only if you sit near the middle on both S/N and J/P, which is rarer than being near the middle on one axis. More often, one result came from work and the other from time alone.
Both decide by logic, the T. ISTJ applies it to proven procedures; INTP applies it to theories. The difference is what counts as evidence, not whether logic is used.
The four-scenario test scores each area of your life on its own, so instead of one label you see where INTP shows up, where ISTJ does, and which letter is doing the moving.