Are all birth control pills really the same?

I have used the brand Chateal in the past which I loved.. I had no side effects on it. I specifically asked for it when I went to the doctor to get birth control recently after not using it for a year. Well they prescribed me Portia instead which I was confused about but didn't make it a big deal. Well I have been on Portia less than a month and im constantly breaking out, i have period-like cramps constantly, I woke up with a rash on my face, my boobs are always swollen and painful and I'm bloated as fuck. With Chateal I literally experienced NONE of this, so I decided to tell my Dr. I got prescribed Chateal but was given Portia, she told me all BC pills are essentially the same thing just different names. How can this be true when I'm having such a bad reaction to Portia and was fine with Chateal?