I have an SMC 8216C EtherCard Elite16 Ultra combo (TP, AUI, BNC) card which uses the 83C790QF chip. It looks just like the card in the image you posted, except the card in that image only has the TP port populated while my card also has the AUI and BNC parts populated. Is that an actual image of your card, or just one you found on the net? Does your card look exactly like that one? I see very little information about an 8218 version on the net. In any case, if it uses the same 83C790QF chip I would assume it works with the same drivers as the 8216, unless trying them shows otherwise.
I have an 8216C in one system running the packet driver and MTCP. That works fine. I haven't tried using it with NDIS drivers in WFW3.11 or Windows 95.
I am using files I got from an Internet Archive snapshot from 1997.
web.archive.org/web/19970401134836/http://www.smc.com:80/ftpdocs/nics.html#nics/ethernet/8xxx
Elite 16 Ultra series of Ethernet Adapters for 8003, 8013, 8013/A 8216
adf200.exe (8.0K) Elite ADF Configuration file for our MCA adapters
asd700.exe (1007.5K) Latest SuperDisk for Elite/Ultra adapters
dia401.exe (83.4K) Diagnose utility for Elite and Ultra Adapters
gez122.exe (41.8K) New EZSETUP For Elite EtherCard Plus/ Ultra in Dos Ver1.08
gpk115.exe (70.8K) Packet Drvr V11.5 for use with 8/16 Bit Elite/Ultra Adapter.
setjmp.exe (7.8K) Switch setting for most of the Elite Ethernet Line of Cards.
Of those files you probably want gez122.exe if you want to soft-config the card, gpk115.exe if you want the packet driver for DOS, and asd700.exe if you want the NDIS drivers.
Give those a try and see if they work with the 8218 card.