Log-linear regression vs. Poisson 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 quite different but do not understand what's the difference between log-linear regression and Poisson regression? 
I think AdamO and Gung's answer do not explain my question in detail.
From AdamO

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.


Update: I am reading some source code fro R0 package in R. The author was trying to estimate the exponential growth rate using different methods:
 ##details<< method "poisson" uses Poisson regression of incidence.
 ## method "linear" uses linear regression of log(incidence)
 if (reg.met == "linear") {
 tmp <-lm((log(incid)) ~ t, data=epid)
 ...
 } 

 # Method 2 == Poisson regression
 else if (reg.met == "poisson") {
   tmp <- glm(incid ~ t, family=poisson(), data=epid)
   ...
 }

Is there any relationship between linear regression on log scale and poisson regression? what is the reason to use different methods?
 A: A Poisson regression is a regression where the outcome variable consists of non-negative integers, and it is sensible to assume that the variance and mean of the model are the same. 
A log-linear regression is usually a model estimated using linear regression, where the response variable is replaced by a new variable that is the natural logarithm of the of the original response variable. Or, if using a GLM, this is done via a logarithmic link function (essentially the same idea, but the mechanics of fitting the model are the different). 
The Poisson regression and log-linear regression are not the same thing, but are often used for very similar problems, particularly among older statisticians (the Poisson regression model only became widely available in software in the 1980s). 
Most people these days prefer a Poisson regression because it can deal with 0 values, whereas you will get an error using a log-linear regression.
It is possible to use a Poisson regression to model data from a contingency table, where the predictor variables are the dimensions (e.g., row and column labels) of a contingency table. This can be referred to as a log-linear model. Perhaps some people call it a log-linear regression (one of the challenges of statistics is that the language is used rather loosely, but many people act as if the language is precise).
