"A-B Ethernet" usually means the old Allen-Bradley Client-Server Protocol, called CSP or CSPv4.
This protocol implemented the old Programmable Controller Communications Code (PCCC) command set over Ethernet hardware, IP addressing, and TCP transports. PCCC commands had previously been transported by DF1, DH, DHII, DH+, and DH485 networks to various A-B controller families all the way back to the original 1774 PLC.
"A-B Ethernet" is going to be used with SLC or PLC-5 style addressing, for reading and writing data table elements like "N7:10" or "B3:1/5".
ControlLogix uses the modern Rockwell Automation protocol, called the Common Industrial Protocol (CIP) which can be transported by DF1, DH+, ControlNet, DeviceNet, and most importantly the EtherNet/IP transport.
ControlLogix can also use the PCCC command codes to read and write PLC-5 and SLC-500 data tables with addresses like "N7:10", but they do it by transporting the PCCC command code in an EtherNet/IP transport, not a CSPv4 transport. This allows things like session security and multi-hop communication paths.
When ControlLogix talks to ControlLogix, it uses the native ControlLogix objects and commands, and uses the EtherNet/IP protocol exclusively.
SLC-500 and PLC-5E controllers built since about 1999 have a "dual stack" on Ethernet that allows them to simultaneously use the CSPv4 and EtherNet/IP protocols.
No ControlLogix-family controller supports CSPv4. The SLC-5/05 and PLC-5E got forward compatibility instead of the ControlLogix having backward compatibility.
It is vital that you determine if your third-party device uses CSPv4 or EtherNet/IP as the transport protocol if you want it to communicate to a ControlLogix controller.