The language used to describe guardianship/conservatorship is decided purely on the laws of each state. Some call everything a guardianship (guardian of person, guardian of estate) some call everything conservatorship (conservator of person/conservator of estate) and some use both terms (guardian of person/conservator of estate).
Minor guardianships are to take the place of a parent and generally expire naturally when the person turns 18, and can include a financial element, depending on the situation and laws of the state.
Trusts can be created either by private parties or by court orders, again, depending on what is happening.
Again, each state makes laws regarding these subjects and they do vary widely in language and even oversight depending on the particular state’s laws, so generally every is correct, if they know their local laws, but will sound wrong to another person from another jurisdiction.
On the issue of adults under court ordered limitations, there is usually a requirement of some evidence the proposed protected person can’t safely manage their finances which has to be more than “they are bad with money”. It has to be more like they throw 100 dollar bills out of a car window and are surprised when those bills don’t turn into butterflies and fly back to the bank account.
All guardian/conservators in the US are appointed by a court, but there are other ways outside the judicial system to gain/give control to another, but it is again state dependant.
Edited to add: my understanding is that a person cannot consent to a guardian or conservator, but I could be wrong on that.