That's a great question, Tim !
The "EtherNet/IP" driver in RSLinx Classic sends out a broadcast packet with the CIP Command "List Identity". Every device that receives that packet should reply with its Identity Object, which RSLinx uses to create the graphical browse schema.
The "Ethernet Devices" driver, by contrast, makes individual TCP connections to the devices in its station list.
Every 1756-ENBT should work with the "EtherNet/IP" driver in RSLinx Classic. There are certainly specific configuration, network mask, VPN, etc issues that might affect the driver, but as far as I know the 1756-ENBT has always responded to the EtherNet/IP driver browse.
Some devices, including the SLC-5/05 Series A or the 1756-ENET from 20+ years ago, do not support that broadcast packet method and will not appear in the EtherNet/IP driver browse.
This is "as far as I know". There may be some firmware subtleties that are outside my recollection, especially on a Monday morning.