The relationship is simple arithmetic: pre-money plus the new investment equals post-money. If a company negotiates an $8M pre-money and raises $2M, the post-money is $10M, and the new investors own 20% ($2M of $10M). That same $2M raise at a $4M pre-money would cost the founders a third of the company — which is why the pre-money number is the heart of the negotiation. A higher pre-money means less dilution for existing holders and a smaller stake for the new money.
For an angel, it helps to remember that pre-money is the founders' starting ask, while post-money is what actually pins down your ownership. The two move together, but they answer different questions: pre-money is "what do we agree the company is worth today?" and post-money is "what slice does my check buy?" When you come in on a SAFE or convertible note, you usually don't set a pre-money at all — a valuation cap stands in for it until the priced round converts your instrument and a real pre-money gets negotiated.