You getting confused between Combi systems and 'Classic' systems.
(A Combi is still 'indirect' heating, by the way).
In the days of back boilers, the boiler was generally connected directly (via pipes) to the hot water cylinder, so there was no separation between water in the boiler and at the tap, and a single header tank fed the hot cylinder.
That's an original Direct system.
When central heating gets added to that, the water in the radiators is also mixed with the hot water system - so crud from the radiators can come out the tap, and you can't use anti-corrosive additives...
There was an intermediate system (which I can't remember the proper name of) that had a bell- or inverted bucket style baffle in the hot tank, that was supposed to help keep the flow from the boiler separate from the tap supply, but there was no actual barrier and everything still fed off the same header tank.
Indirect systems use a copper coil in the hot tank, to transfer heat from the boiler & heating side without allowing that water to mix with the tap supply.
They use a header for the tap water supply to the tank, and a smaller header (or sometimes a pressurised / sealed system) for the boiler & radiator circuit.
A combi is actually a small version of that system.
They have a (very small) internal tank for the hot tap water reserve, with a heat exchanger coil fed from the separate, sealed, boiler & heating circuit.
The main difference is that the boiler heat output modulates, together with the diverter valve operating, to give the required hot water temperature rather than just switching a boiler on & off via a thermostat with the big hot tank setup.
Edit - I'm only referring to hot water / heating systems above, not direct/indirect cold water.