These are both standards used in archival arrangement. Below is a simple introduction into these two terms. There are other variables of consideration for each that are not included here.
Provenance:
Refers to ownership and creation - the chain of custody. Sometimes it can be a person or a place.
An easy way to understand this standard: A document created by Dr. Steven Burg should be kept with the folder or collection of Dr. Burg. A document created by the President's Office belongs in the President's record group.
Original Order:
The act of preserving the order in which the documents were placed by the creator. (respect des fonds) The principle behind this standard is that materials should not be reordered for the convenience of researchers or the archivist.
Original order can be the most difficult standard to honor. You could receive a collection that doesn't appear to have any kind of order, especially not any that provides an insight into the creators priorities. You could be given a collection that was already handled by someone else who has disrupted the original order of the creator. These are most common challenges of maintaining original order.
Always remember: Theories are great but can be different in practice.