The arithmetic is simple — post-money equals pre-money plus the investment — but which one a conversation is using changes how much of the company you hand over. An investor's ownership is always their cheque divided by the post-money valuation. So "$2,000,000 at $8,000,000" means 20% if that $8,000,000 is pre-money, and 25% if it is post-money. Same sentence, five points of your company.
Founders lose real ownership to this ambiguity, usually by hearing the bigger number and assuming it is the one that flatters them. Always ask which figure is being quoted and restate it as a percentage before agreeing to anything. The percentage is the only thing that is unambiguous. It is also worth checking whether a new or expanded option pool is being counted inside the pre-money figure — that convention, common in venture deals, means the pool dilutes you rather than the incoming investor.
A concrete example: you agree to raise $1,000,000 at a $4,000,000 valuation. If pre-money, post-money is $5,000,000 and the investor owns 20%. If post-money, the pre-money was $3,000,000 and the investor owns 25%. On a company you eventually sell for $20,000,000, that difference is $1,000,000 — decided by one word in an email nobody clarified.