I expect that that most lawyers can explain the difference between the "burden of proof" and the "standard of proof".  Some lawyers might be more challenged in distinguishing between "standard of proof" and "standard of "review".  Others might struggle to explain whether "substantial evidence" and "preponderance of the evidence" are the same.  Conveniently, the Nevada Supreme Court has explained it all in a succinct opinion issued yesterday that addresses how each of these terms are applied in the administrative context.  Nassiri v. Chiropractic Physicians' Bd. of Nev., 130 Nev. Adv. Op. 27 (2014).

Burden of Proof/Standard of Proof

"'Burden of proof" refers broadly to a party's duty to present evidence and argument to prove his or her allegations, whereas 'standard of proof' refers to the 'degree or level of proof demanded' to prove a specific allegation".

Standard of Proof/Standard of Review

The standard of review is the standard that a reviewing court applies to determinations of administrative agencies.

Substantial Evidence/Preponderance of the Evidence

"Substantial evidence" is that standard of review that refers to the quality and quantity of evidence necessary to support factual determinations by an administrative agency.  "Preponderance of the evidence" is a standard of proof.