Hi Frank,
I thought I knew the answer to your question, and this Lowes article confirms it.
https://www.lowes.com/n/buying-guide/compound-miter-saw-buying-guide
A compound miter saw is one that can swivel left and right to cut angles and can tilt in a single direction.
A double bevel or double compound miter saw is one that can tilt in both directions. It make it a little easier to make various cuts. You can make all the same cuts on a compound miter saw, but you may need to flip the wood around when cutting the opposite angles.
In my opinion the double compound is not needed and I would not specifically look to get one, but if the price was the same or close, it would be handy to have.
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