A Guardianship is probably broader than the rights given to the agent under either a "Financial" or "Medical" POA. A Guardian is formally appointed as such, by a probate judge, and that Guardian then has formal reporting requirements. An agent under a Financial POA probably has reporting requirements as well, but is not under the obligation to report on the court's schedule. A Guardian has authority to make decisions about the "ward's" housing, medical, education, general welfare, etc.
By contrast, a Conservator's role is limited to the management of assets, and entering into contracts. For example, if a person is incapacitated due to a brain injury, in an accident, a conservator would be the one to consult with, in terms of setting up an attorney-client relationship with personal injury counsel. There are other similar business roles that a Conservator might take on, as well.
An agent's role under what I call a "Medical POA" is limited to medical care and end-of-life decisions, for the principal, after the principal is no longer able to make those decisions for themselves.
Many times, the existence of a well-drafted POA makes the formal appointment of a Guardian/Conservator unnecessary. However, sometimes, getting the probate court to formally appoint a Guardian/Conservator provides clarity to a situation, where authority to act is unclear.