Well, it's one of those situations in which we all know the situation, and what is being said, so I'm not sure that the words matter too much.Surely Economy 7 is the system. The tariff can be increased (price rise).
I guess it depends upon what one means by 'the system'. The electricity supply to the property is obviously the same whether it is E7 or not. It's the meter and any load switching which turn it potentially into an 'E7 system' - but, as has been said, there are different flavours of E7.
However, I think it's understandable that eric regards E7 as a 'tariff - since the tariff doesn't just determine 'a price', but it determines the prices for peak and off-peak electricity. If, hypothetically, those two figures were the same, then it wouldn't be functionally E7, even if 'the system' (meter etc.) was "E7" - so it could be said that, by specifying a lower price for off-peak electricity, the tariff is, in some senses, what makes it (functionally) E7!
Kind Regards, John