Actually, Minutes are usually a summary of the discussions and the actions that are to be taken and the people responsible for the actions. Minutes are brief.
A report will depend on the organisational requirement and the intended purpose and audience and will contain more detail. Minutes help guide what is in a report but a report could include discussion points and more detail.
if you wanted a word for word account of a meeting, you would ask for a transcript as this is what it really is. In high level meetings this could be required for future accountability, and most likely would be recorded by being taped and then written out later.
That's my educated opinion anyway.