How family=Poisson works in glm function in R?

[KNR]

Let's assume I am working with this dataset on R:

n <- 40
x1 <- rnorm(n, mean=3, sd=1)
x2 <- rnorm(n, mean=4, sd=1.25)
y <- 2*x1 + 3*x2 + rnorm(n, mean=2, sd=1)
mydata <- data.frame(x1, x2, y)

I cannot understand how Poisson regression works in R, I would assume that the following are equivalent:

mod <- glm(y ~ x1 + x2, data=mydata, family=poisson())

mod <- lm(log(y) ~ x1 + x2, data=mydata)

But they are not. Why? Did I misunderstood what Poisson regression is in the first place?

 

[Buckeye]

Poisson regression is often used to model count data (taking values: 0, 1, 2, 3). Poisson regression also models rates (you can supply an offset to the model for this purpose). For example, the number of patients arriving at a hospital within a given day. Your dependent variable is not a count variable. At best, the first code is modeling y as a rate. But, I'm not too sure. The second piece of code is just a linear, OLS model with a logged dependent variable. It has no relation to a Poisson regression model.

 

[fed2]

there actually is a relationship between poisson regression and log-normal models, in that lognormals are often used to approximate poisson models, to varying degrees of success. read all about it. https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/j.2041-210X.2010.00021.x