In the most extreme cases, waves and holes are clearly different water features. An example of a wave that is clearly 'not a hole' is any standing wave without any backwash (no whitewater at the crest where the wave is breaking). An example of a hole that is clearly 'not a wave' is what is found when water is dropping almost vertically over an obstruction and produces a large backwash as can be found at the base of a waterfall or a low head dam.
A feature can still be considered a wave even if the wave is breaking (producing a backwash/foam pile) but there will always need to be a clearly visible trough of green water and some green water on the 'face' of the downstream part of the feature.
There is a grey area where a feature might be considered a wave by some and a hole by others. (These are sometimes called 'wave-holes'). This is when there is a visible green water trough in the feature, but a large foam pile with little green water visible on the downstream face of the feature. Typically this type of feature is ideal for playboating and thus most artificially constructed play spots look like this.
"I just want to thank everyone who made this day necessary." -Yogi Berra
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