What is the difference between Apply Measure Now and Drop Measure from Library to create a New Always Run Measure ?

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"Apply Measure Now" applies the measure to your live model, if you save the model the changes from the measure will be in the model.

Measures added to the Measures Tab are applied at run time as part of the simulation workflow. You won't see the changes in the OSM file you are working on MyModel.osm for example, but if you look for in.osm file in your run directory it will reflect the changes caused by the measure.

There may be use case where you want to apply the measure directly, for example to automate a task instead of modeling by hand, but you want to see and inspect and possibly change it. Other times you may want to keep it in the workflow for runtime, for example when you may want to run it again later with different arguments.

Also note that Apply Measures Now are only for OpenStudio Measures. If you want to apply an EnergyPlus or Reporting measure that has to be done as part of the runtime workflow.