How are proteins formed?
Essentially, yes, "proteins that we consume form new proteins that are different".

The processes are each of them topics for themselves. In short, consumed proteins are digested by peptidases (enzymes) in the stomach, breaking them down into their consituent amino acids. These are absorbed in the gut and transported in the blood to all cells. These take up amino acids and attach them to tRNA molecules which are used in translation to form new body proteins.