Diagram 13: Comparison
Compared with 'a', Black 1 is more urgent. If, however, Black had a small-knight enclosure with 'b', then Black 'a' would now be the more urgent move.

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[go]$$B Corner
$$ ------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . O . 1 . . b . . . . |
$$ . . , . . . . X , X . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . a . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |[/go]

Regarding the second sentence, is this because without the small-knight enclosure White can slide nearby or under the black stones by playing at or adjacent to b on the third line?

White would play to the right of 1 usually, just to reduce the corner at the "open skirt" but the idea is the one you have already. Playing directly at b would be too tight, probably, at least for the time being-

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White would play here, which both makes a 2 space extension to make a base for his stone, and also has nice follow-ups at a or b to annoy black's corner so could be sente. Note that in the original diagram also has a nice follow-up of pincering white's top side stone (if there is no support off the edge of the board) so has some sente feeling too.

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[go]$$W Corner
$$ ------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . a . . . . |
$$ . . O . . 1 . . b . . . |
$$ . . , . . . . X , X . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |[/go]

I would also add that with the low enclosure as below, although extending on the right is (locally) a little bigger than the top (globally the top could be bigger if that white stone is more important than the one on the right), they are both neither particularly urgent and much less important than the original black 1. That's because white playing at either of those points is not particularly annoying (no powerful follow up) and you can easily tenuki, though if white got both a and b you might feel like jumping out to c to make sure there's no funny business in the corner and not get surrounded. You might not like white getting the second extension in sente, so you might answer white extending on one side with extending on the other (particularly if your extension has a follow-up against the white stone there) which is basically treating the two sides as miai, but with the high enclosure they most definitely aren't miai as the top is 4th line so white there is annoying.

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[go]$$B Corner
$$ ------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . O . . a . X . . . . |
$$ . . , . . . . . , X . . |
$$ . . . . . . . c . . . . |
$$ . . . . . . . . . b . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |[/go]