Is there a relationship between log(response variable) and glm(family="gaussian")?

Does glm,glmnet(family=gaussian) have any relationship ?
with log(target)?

Also, I see people who log-transform the prediction target to make it look like a normal distribution, but since linear regression models expect the "model residues to be normally distributed", doesn't it make sense to "transform the prediction target to a normal distribution"?

I would also like to know why the family of glm can specify other distributions.