Economy 7 is a tariff. How it is used varies. Somewhere there will be a method to work out at what time the power is used. This was originally done with a white meter and the two supplies were separate. But then it was combined and each appliance had it's own timer so Washing Machines, Tumble driers, Dish Washers, Immersion heaters could all take advantage of the cheap rate power. There was also an Economy 10 which had a day time period to boost the storage heaters.
Large consumers factories and the like with offices attached found the use of storage heaters very good as they could run on a smaller supply. But for houses it did not work very well as by time people arrived home there was very little heat left in the old bricks.
There were some bulk storage units which look like normal central heating and the heat was stored in one central unit. These worked a lot better.
So the answer is no there are not different types of Economy 7 but there are many types of storage systems, tariffs and control methods. So to be less pedantic the answer would be yes as I would think you were referring generally to storage system rather than one tariff type.