The simplest answer is finances and everything else. Conservatorship only deals with finances and does not grant any power to make medical, housing, personal, etc., decisions. Whereas guardianship does not give any authority to handle finances, with the possible exception of the power to contract and the power to apply for government benefits.
Keep in mind that different states call these powers different names and Minnesota has also changed the name over time. Prior to the passing of the Uniform Guardianship and Protective Proceedings Act in 2003, conservatorship used to be referred to as “guardianship of the estate” and guardianship used to be titled “guardianship of the person.”
Also, be aware of the subtle difference in terminology regarding a person under guardianship versus a person under conservatorship. An individual who has a guardian appointed to protect his or her person is referred to as a “ward.” An individual who has a conservator appointed to protect his or her assets is referred to as a “protected person.”
The difference in terminology may reflect the fact that a ward is declared to be incapacitated when a guardian is appointed, whereas a protected person is not declared to be incapacitated. Conservatorship appointment by the court only declares the protected person to: (1) be unable to receive and evaluate information; and (2) have assets at risk of waste or loss. In cases where both a guardian and a conservator are appointed, the individual is usually referred to as the ward and protected person.