Fixed Frequency

Fixed frequency monitors have been designed to work with a defined horizontal refresh rate and vertical refresh rate. Any video signals that do not fall within a narrow margin of these designed frequencies will cause the monitor display to be useless. Generally horizontal or vertical hold (or both) will be gone, possibly the monitor will notice things are bad and shutdown.
If this is hard to understand, maybe you need to know more about
how monitors work.

Multiple Frequency

Multiple Frequency monitors have been designed to work with a small number of fixed frequencies (see
Fixed Frequency monitors)
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Multi-sync

Multi-sync monitors will examine the incoming video signals and determine from them what horizontal and vertical frequencies to use. This could be viewed as either a
multiple frequency monitor with a very large number of frequencies to choose from or as a fixed frequency monitor with a very wide margin of tolerance.
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Sync on Green

"Sync on Green" is the term used to refer to the practise of using the green video signal line to send the
composite sync pulses to the monitor. This does not cause interfearance with the video signal because sync pulses are only sent during the "blanking" period when there is no video signal going to the monitor anyway.
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Composite Sync

Composite Sync is what happens when the horizontal sync signal and the vertical sync signal are combined into the one "composite" signal. This works because the vertical sync pulse is much longer than the horizontal sync pulse and there are no horizontal sync pulses required during the vertical sync period. This requires only one wire for both the sync signals.
If this is hard to understand, maybe you need to know more about
how monitors work.

Separate Sync

The most basic method of sending the synchronization pulses to a monitor is to use a different wire for the horizontal and the vertical sync pulses.
If this is hard to understand, maybe you need to know more about
how monitors work.