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).