PC/SC and contactless card ATS

I was recently puzzled by the different ATS values returned by my Omnikey Cardman 5321 (connected to PC) and my NXP PN531 (connected to embedded system). I tried with both the Nokia 6131 NFC and an NXP JCOP31 smart card; here's what the output looked like (all hex):

Nokia 6131 ...
... with PN531:

SENS_RES    0200
SEL_RES     38
NFCIDLENGTH 4
NFCID1      5039F5A8
ATS         0D 78 80 84 02 00 73 C8 40 13 00 90 00            .x....s.@....

... and with Cardman 5321:

(same NFCID1)
ATR         3B 88 80 01 00 73 C8 40 13 00 90 00 71

Smart card:
... with PN531:

SENS_RES    0400
SEL_RES     28
NFCIDLENGTH 4
NFCID1      E0742A86
ATS         0D 38 33 B1 4A 43 4F 50 33 31 56 32 32            .83.JCOP31V22

... and with Cardman 5321:

(again, NFCID1 is similar)
ATR         3B 89 80 01 4A 43 4F 50 33 31 56 32 32 4A

After scratching my head for a while I gave in and RTFM for the Cardman reader. And I was reminded again that glossing over details is never good, because in fact ATS != ATR. The PC/SC standard (PC/SC v2.01 “Interoperability Specification for ICCs and Personal Computer Systems”) requires that the driver convert the received ATS to an ATR.

The PC/SC specifications can be downloaded here.