Generally yes, they were issued by type to units but not always! The obvious problem came when issuing Fireflies to a unit equipped with Sherman III, M4A2 as there was no Sherman IIIc and so units had a mix of diesel and petrol vehicles.
According to research by Peter Brown, the following were held in June 1944.
11th AD Sherman V and Vc
Gds AD Sherman V and Vc
4 AB Sherman II and Vc
8AB Sherman II DD, III and Vc
27AB Sherman III, V DD and Vc
30 AB Sherman V and V crab
33AB Sherman I, II and Vc
1TB Sherman I and II
4 Cdn AD Sherman V and Vc
2 Cdn AB Sherman III, V DD and Vc
Polish AD Sherman V, Ic and Vc
I think the 8AB Sherman II DD should be III DD.
Later on, I suspect the mix became greater, certainly the number of 17 pdr tanks increased. There were also a few OP and ARVs scattered throught the formations, usually of a similar fuel to the gun tanks but not exclusively.