A person could be gaining weight because they are gaining muscle, not fat. Or, if female, they could be gaining weight because they are pregnant. So, the two statements do have different meanings. If a person is putting on weight because they are increasing the fat content of their body, "I am getting fat" is an accurate statement - "these days" is not necessary. Derek B makes a good point about gaining weight not necessarily making a person fat. If a person is slim, adding a little fat is not going to make them fat.

As Ramin said, they are both about the same. If you wanted to "get technical" about it, there is a slight difference. "I'm gaining weight these days" (notice the "s" at the end of day) = I weigh more recently than I did before. "I'm getting fat these days" = Recently I have become overweight You can gain weight without reaching the stage of being fat.

I suppose both are correct and sort of same.