Neil, there seems to be some confusion here.
The E288CC and ECC88/ ECC83 are double triodes, that is two separate devices enclosed in a single glass envelope. Does your tester, test each triode separately? The pin connections for the first triode are:
anode, pin 1
grid, pin 2
cathode, pin 3,
and for the second triode:
anode, pin 6
grid, pin 7
cathode, pin 8.
The heaters are attached to pins 4 and 5. Heater voltage is 6.3V (that's what the 'E' means in the nomenclature) and the heater current will be 475mA (roughly 30 -60% more than for the ECC83 and ECC88).
No, the anode is not the same as the filament. I'm trying to find a simple to read guide on vacuum tube parameters, so that you can understand/interpret the data sheets that Mike has sent you. This is not really my field; I'm a 'sandman', to use the current colloquialism and I has been fourty years since I last built a valve amp. If all else fails you could try the 'World Design' forum; the people there seem to be more DIY with valve circuits and will be able to help you.
Regards
Barry