A good question, because the difference is a hairline one !! Both as you rightly say focus on energy saving.
The ECM is generally with reference to energy savings in a building - includes structural changes, fixtures and fittings, and practices that hope to make savings across the building setup.
The EMO refers to short, medium and long term user practices aimed at energy saving. The context here is entirely to do with regularity and lifestyle practices, and apply to setups regardless of whether ECM's have been organised for the specific building or not !
Energy management opportunities represents the areas where we can save energy such as zero net energy buildings, harvesting waste heat from the environment, solid waste to energy conversion, etc.
Energy management measures specify how energy management can be quantified. For example, how many watts of electric power can be saved by using Energy Star light bulbs instead of the incandescent light bulbs or how much energy efficiency can be gained by using combined cycle plants instead of the traditional fossil-fired power plants and so forth.
In addition to the previous, search about the energy management hierarchy. Energy management includes three main areas: 1) Energy conservation, related measurements and opportunities , 2) Improving energy efficiency and 3) Usage of renewable energy.
In Energy Management Handbook by Turner I found another definition that might clear the issue. The definition of energy management is the efficient and effective use of energy to maximize profits (minimize costs) and enhance competitive positions. i.e. the final target of energy management program is to save money.
Therefore, ECO’s could be objectives of energy management program which can be implemented to produce a cost saving.