What Is the Fundamental Difference in Security Guarantees between Proof-of-Work and Proof-of-Stake?

Proof-of-Work (PoW) guarantees security through energy expenditure and computational power, making attacks economically prohibitive due to operational costs. Proof-of-Stake (PoS) guarantees security through economic incentives and penalties.

Attackers risk having their staked capital (the underlying asset) "slashed" and losing the value of their investment, making attacks prohibitively expensive in terms of capital cost.