I want to use a holding tank to supply fresh water for a flush and outside shower at my cottage in a bunk house. Is there a demand pump I can use instead of having a holding tank with a pressure switch? If so what is the pump called?

You can buy a booster pump. They frequently come with a one or two gallon pressure tank attached. Since you don't seem to be describing a high demand situation, that might work well for you.

First you ask,

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I want to use a holding tank to supply fresh water

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and then you ask,

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is there a demand pump I can use instead of having a holding tank

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Yes a booster pump could be set up on a demand basis.
Where would the supply for this demand pump come from? Back to you, Tom

It is a little confusing. In your heading, you describe a "pressurized holding tank." If the water in the tank is under pressure, you don't need a pump.