What thermal store?
1)Buffer tanks and thermal stores are similar . The difference really is how they are used and the number and type of heating sources that are connected to them.
Thermal stores are normally directly connected to the (biomass) boiler and indirectly connected to the solar (coil) looks like your big green tank has two coils one for the boiler and one for solar. Additional the hot water would normall be heated via a coil or plate heat exchanger from the thermal store, so you with a thermal store it is not usual to have a store of Domestic Hot water - it is heated on demand.
from the pictures you've posted it doesn't look as if your big green tank is a thermal store, it looks like a large Domestic Hpt Water (DHW) Cylinder.
Buffer tanks are directly connected to the heating source (biomass boiler in your case) and then the heat for the Heating and DHW are drawn from the buffer tank.
2) DHW cylinders with Solar thermal input would normally have a volume dedicated to the Solar - i.e the volume associated with the bottom coild hence they will always be larger than a DHW cylinder heated only by a boiler.
Heres a thermal store configuration:
:: AKVA SOLAR
3) Down to quality, and what they're designed for. Flow rate, nominal pressure, differential pressure, leak rate etc.
Much more information and we're going to have to start charging you
Ask for a copy of the hydraulic design from your installer (we always do one so that the plumbers put everything in correctly )