A facsimile is a published reproduction of a manuscript.
A critical edition is prepared by scholars, based on the evaluation of all known primary source versions of a piece, ie., manuscript versions and the first edition, possibly other important early editions. A critical edition is designed to present the most authoritative version of a piece. Includes extensive commentary identifying manuscript sources consulted, as well as explanations of editorial decisions.
A scholarly edition is prepared by scholars, based on the evaluation of relevant primary source versions of a piece. Like a critical edition, it will include commentary identifying manuscript sources consulted, as well as explanations of editorial decisions.
Performance editions are often produced from unstated or secondary sources (other published versions of the piece), and may incorporate additions or changes designed to help the modern performer.
Publishers apply this term liberally. An urtext edition typically refers to a type of scholarly edition designed for performance. Aims to present the original musical text, without excessive editorial additions or changes. Often will include commentary from any editors.