I have asked questions about this before. Scarce means fewer than a common coin but more of them than a coin rated rare. It is a limbo coin. Easyer to get than a rare coin if that makes any sense.
I've developed my own thinking on this as follows
I consider
scarce to mean a coin that, if you
search for it for a year, you will find one or more at a reasonable
price, ie at its generally accepted market value (though you may not buy it).
And
rare means a coin that you have a low chance of finding at a reasonable
price, ie at its generally accepted market value, even if you
search for a year. You might see one or two examples in a year, but not at a reasonable
price.
And extremely
rare means you might wait a decade to find a single example of the
type and
still not be able to buy it at what you consider to be it's market value.
Common means a coin
type you can find today or within a few weeks if you look in all the usual places.
Very common means a coin you can find multiple examples at retail at any one time.