In general, the CONEMP or COE, concept of employment, is more detailed and usually more tactically focused.  It involves the use of forces which differs from CONOPS, concept of operations, which involves a broader scope of the commander's intent on how to apply all available resources.  Our experience is that the USMC writes a detailed CONEMP in place of the Operational Mode Summary/Mission Profiles (OMS/MP.)

A Rand Report completed for the USAF in 2003 described it this way:

LACING THEM TOGETHER

Now to lace the levels, actors, and concepts together (from the bottom up):

•  Combatants accomplish a portfolio of military tasks (according to the CONEX for each stated task). By doing so, they enable a subordinate commander (in the presence of a CONEMP) to achieve some stated operational objective (or to conduct some stated major operation within a campaign).

•  Subordinate commanders achieve a portfolio of operational objectives (according to the CONEMP for each objective). By doing so, they enable the overall combatant commander (in the presence of a campaign strategy) to attain the effects desired in conducting the campaign.

And from the DOD Dictionary of Terms and Definitions.

concept of operations — A verbal or graphic statement that clearly and concisely expresses what the commander intends to accomplish and how it will be done using

available resources. Also called CONOPS. (JP 5-0)

operation — 1. A sequence of tactical actions with a common purpose or unifying theme. (JP 1) 2. A military action or the carrying out of a strategic, operational, tactical, service, training, or administrative military mission. (JP 3-0)

employment — The strategic, operational, or tactical use of forces. (JP 5-0)