Why the card's ATR is different from a product to another one or from a firmware version to another one?

Why the card's ATR is different from a product to another one or from a firmware version to another one?

The ATR of a wired-logic storage card is constructed according to a list of card technologies maintained by the PC/SC workgroup

Let's use the MiFare UltraLight example, new versions of this list are published regularly, some couplers used to implement the 2005 version, where only the UltraLight is referenced.
Hence all cards that look more or less like a Mifare UL return NN = 00 03 "MIFARE UltraLight".

Today's couplers (CrazyWriter HSP for example) implements the 2011 version, where the UltraLight C has been added.
Cards that look more or less like a Mifare UL but with more than 16 pages return NN = 00 3A "MIFARE UltraLight C"

Tomorrow's products (including next version of CrazyWriter HSP firmware) will implement the last version at the date of release.
Today it would be the 2013 version, where the UltraLight EV1 has been added under NN = 00 3D.

How can I authenticate/read/write/access data on my card with my SpringCard reader?

There is no easy answer: this fully depends on your card and your SpringCard reader. You should first read the documentation of your card, then you should download and read the developer's reference manual, or the developer's guide of your product, from our main website. This should give you all the information you need.
If you don't know how to start, you can check this page in our blog. It explains in detail how to read and write the content of a Mifare Ultralight card, with a Prox'N'Roll PC/SC: having read the above-mentioned documentation, you should be able to easily adapt those steps to your specific situation.

I have several cards, from different manufacturers. How can I differentiate them? How can I retrieve their characteristics?

If your reader is from the CSB6 Family (CSB6Prox’N’Roll PC/SCEasyFinger and CrazyWriter), we provide a free software application in our "SDK for PC/SC" (link: https://www.springcard.com/fr/download/sdks) named "PC/SC Diagnostic".

Please open this application and putt a card on your reader then you will be able to read the ATR's card.
With this ATR number go to this website : http://ludovic.rousseau.free.fr/softwares/pcsc-tools/smartcard_list.txt, and search it.

It will be return the informations you need.

What is an ATR?

An ATR is a series of bits sent by the card to identify itself. The reader recreates it for all contactless cards. In some rare cases (like the Calypso SAMs), the serial number is available in the ATR. Please note that you shouldn't trust an ATR to determine with certainty which card you're communicating with.