Aren't all pitchers shut down on their rest days?

No, this is not playing games with words.  We baseball fans miss stuff that's been staring us in the face all along.

I've written posts recently about New York pitchers possibly getting shut down: Matt Harvey, Noah Syndergaard, Luis Severino.  Also mentioned: Stephen Strasburg, who was shut down in 2012 by Washington.

Shutting down means having a pitcher not pitch to prevent injury.

The typical fan reaction to this is usually: just rub your arm in the dirt and get out there and pitch whenever you're told to, you pampered, self-centered, over paid prima donna.  Media reaction is even more reactionary.

The Yankees signed Masahiro Tanaka (born Nov. 1, 1988) for big bucks to a seven year contract starting in 2014.  Tanaka threw 1,315 regular season innings pitching in Japan from 2007 through 2013.  Tanaka was accustomed to pitching once a week.  In the U.S. Tanaka has missed time with arm injuries.  His Yankee innings:
2014: 135
2015: 143

Yesterday in a "must win" game against first place Toronto at Yankee Stadium Tanaka pitched 7 shutout innings and threw 107 pitches.  Tonight the Yankees play the Rays in Tampa but CC Sabathia will be on the mound, not Tanaka.

Tanaka will rest at least four days before pitching again.  In other words, the Yankees are shutting down Tanaka so that he will not be injured.

Tanaka's Days of Rest from baseball-reference.com:
2014:

I	Split	W	L	W-L%	ERA	G	GS	GF	CG	SHO	SV	IP	H	R	ER	HR	BB	IBB	SO	HBP	BK	WP	BF	WHIP	SO9	SO/W
	4 Days,GS	4	2	.667	3.07	8	8	0	1	1	0	55.2	51	19	19	6	10	0	53	2	0	1	223	1.096	8.6	5.30
	5 Days,GS	6	3	.667	2.98	9	9	0	2	0	0	60.1	59	24	20	8	10	0	66	1	0	3	244	1.144	9.8	6.60
	6+ Days,GS	3	0	1.000	1.33	3	3	0	0	0	0	20.1	13	4	3	1	1	0	22	1	0	0	75	0.689	9.7	22.00

2015:

I	Split	W	L	W-L%	ERA	G	GS	GF	CG	SHO	SV	IP	H	R	ER	HR	BB	IBB	SO	HBP	BK	WP	BF	WHIP	SO9	SO/W
	4 Days,GS	2	1	.667	2.45	4	4	0	0	0	0	25.2	16	7	7	3	3	0	23	0	0	1	94	0.740	8.1	7.67
	5 Days,GS	7	4	.636	3.51	14	14	0	1	0	0	92.1	82	41	36	15	18	0	80	1	0	3	373	1.083	7.8	4.44
	6+ Days,GS	3	1	.750	3.96	4	4	0	0	0	0	25.0	18	12	11	4	5	0	29	0	0	0	98	0.920	10.4	5.80

In 2014 the Yankees started Tanaka on four days rest in 8 of 20 starts.  In 2015 that has shrunk to 4 of 22.  The Yankees are shutting down Tanaka for longer intervals.

This type of short term shut down is familiar to us, so we do not question it.  We're comfortable with it.  No one is asking Tanaka to be heroic and demand the ball for tonight's game.

So what is different about shutting down a pitcher four or more days versus four or more months?