The battery connector was changed between T4x and T6x generation, so the batteries are incompatible.
The original Ultrabay Slim Battery
works in all the laptops mentioned in the Thinkwiki page
The Advanced Ultrabay Battery
was later rebranded as Thinkpad Battery 42
. It works in the machines mentioned here
plus the T420s series. Note that as it says - the battery has been discontinued.
The Thinkpad Battery 43
is the newer revision of the Battery 42. It is the same except has the chip that makes it work in T430s, and is fully backwards compatible. It works with all the systems listed in the Lenovo reference page