As I understand it, the "federal" system in most countries has a lot of power -- such as a national sales tax, national education system, national health care, national law enforcement, national regulations (versus national "minumums" in the United States), and so on.
For example, the GST or VAT is a national sales tax used for national programs. The United States could not have such a tax without a change to our Constitution, which requires approval of three-fourths of the states. (Switzerland has an "easier" two-thirds requirement for national referendums on Constitutional matters.) It was a long battle just to have a federal income tax in the United States. Even today,
people debate if the Amendment was passed properly.
I also believe a teaching certificate is good nation-wide in most countries. In the United States, my California credential was accepted by two states, as long as I took some additional courses. California accepts no other states' (at this time) without additional training because we had a "bilingual" or "language acquisition" requirement. (There is a move to have national credentials, but states would be
free to "add" to the minimums, meaning the "national" would still not be good enough for all states!)
The EPA is our "Environmental Protection Agency" at the federal level. California has another EPA (Cal-EPA) which has even stricter standards for air and water pollution, mainly to cope with our geography, which includes two highly-contained valleys, L.A. and the San Joaquin, where air pollution collects. The "national" standard would not help us enough -- so our standard is different.
(Cars sold in California are "different" than in other states: emission controls are like the Canadian models on steroids, as Susan can attest. Her "Canadian" car doesn't meet California standards, but surpasses U.S. minimums.)
California's laws are often more strict than the minimums of the United States. Our labor laws, for example, have an eight-hour workday and a 40-hour week. National law only protects the 40-hour week. (The eight-hour day is a problem in California, where some people wanted to work four ten-hour days a week and it turned out to be a violation of the law.)
The amendment to the U.S. Constitution must be approved by three-fourths of states. The amendment as passed may specify whether the bill must be passed by the state legislatures or by a state convention. Amendments are sent to the legislatures of the states by default.
It is interesting to note that at no point does the President have a role in the formal amendment process (though he would be free to make his opinion known). He cannot veto an amendment proposal, nor a ratification.
Any state my propose an Amendment, but it must be approved by both houses of Congress before being submitted to the States.
Amendments set minimum standards for all states, or establish the protected rights of the people.