What are Orchestral Recording and Close Miking?  What are the Differences?

Orchestral recording is just what the name implies: Making a recording (particularly of an orchestra, but the technique works for smaller aggregations) with a minimum of microphones.  They are placed to capture the audio (music and room acoustics) as it would be heard, under optimum conditions, from the best seat in the house.  Microphones are usually placed at some distance from the musicians, where there is a balanced acoustic mix of the musicians and the room acoustics.  The output of the microphones is typically recorded as a stereo track which, probably after some post-production processing, becomes the stereo master.

Close miking, in its purist form, involves placing microphones close to the musical instrument so as to pick up the sound of that instrument with a minimum of sound from the environment (room acoustics, noise, etc.) and from other instruments. Except in the case of soloists, this usually involves several microphones, often one or more per instrument, and either a mixing console or a multitrack recorder.  The multitrack recording is mixed down in post-production, usually to a stereo master.  The ultimate in close miking of an electronic instrument, like a keyboard, is not to use a microphone at all, but rather to use a "direct box," which connects the electrical signal generated by the instrument directly to an input of a recorder or mixer.

There are, in fact, an infinite number of combinations and variations of these techniques. You may add "spot mics" which are close miking instruments (or vocalists) in the orchestra/band that may not be picked up well by the orchestral mics, and (usually) record them on separate tracks to be mixed down in post-production.  Or, conversely, a set of stereo "ambiance" microphones may be added to a close-miked session, in order to capture the acoustics of the space and add some of the room character to the final mix.