To expand on it: I can't really compare the magnitude, because I don't have a good sense for how much of an issue it is in the US, but yes, states do sometimes disagree with each other, have differing interests depending on local factors, want funding allocated to their projects, and they do occasionally squabble with the federal government over authority (especially when they want federal funding for things that are their area of responsibility). They also have quite an effect on how politics inside and between the political parties work (which I feel like in other countries the largest cities do instead?)
For reference, do you hear about any internal German politics?