There is a powerful, and statistical way of thinking about all regressions. Instead of viewing regression as simply “minimizing the least squares error”, or some type of MLE, we can instead think about the statistical, generative model of our process.
This is the approach to regression that talks about $\Beta$, normal distribution, and the residuals are normally distributed!
Essentially, Poisson regression simply makes a different modelling assumption/perspective: that we look at a $ln$ viewpoint!
And more generally, we can use it to discuss other types of regression too.
https://en.wikipedia.org/wiki/Poisson_regression https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Poisson_Regression.pdf