Log-linear regression vs. Poission regression

In this post, OP asked the difference between log linear regression and logistic regression. Two answers in the post are very clear and directly address OP's question.

I understand Log-linear regression and logistic regression are quirete different but not understand what's the difference between log-linear regression and Poission regression?

I think AdamO and Gung's answer are not explain my question in detail.

the log-linear model is actually just a Poisson regression model

From Gung

"log-linear regression" is usually understood to be a Poisson GLiM applied to multi-way contingency tables.

• That's weird. I've always understood "log-linear regression" to mean linear regression where the dependent variable is the log-transformed variable of interest (something positive-valued). Which is obviously different from Poisson regression. But if there is some ambiguity, you have to say what you mean by log-linear regression before anyone can explain the difference from Poisson regression. – The Laconic Feb 14 '17 at 20:51
• I find "log-linear regression" to be somewhat of a misnomer since the whole idea extends to much more than just plain regression (probably why wikipedia calls it log-linear analysis. Log-linear analysis is a form of categorical data analysis mostly used with three-way contingency tables. A common Poisson GLM would only explain a subset of the independence relations that a log-linear analysis can explain, though in some cases (e.g. two-way tables) both methods are exactly the same. – Digio Dec 4 '17 at 11:35