Capital market is very broad. It includes a variety of assets - stocks, bonds, etc.
Money market refers to short term assets like bonds with maturities coming soon. Money market funds hold these short term securities.
Money market funds hold highly liquid assets and offer daily liquidity.
Agency market: someone acts on your behalf to execute the trade. For example, you might pay commissions to use someone's trading algorithm for an equity trade.
Dealer market: you transact with a market maker. Rather than earn a commission, the market maker tries to make money by buying from some people and selling to another and a higher price. The dealer temporarily owns the security and takes some risk that the price may change before selling.
Agency markets tend to be more liquid. Dealer markets are more common for art, fixed income, etc.