The labels are misleading - they describe style, not location. An American-style option can be exercised at any point up to expiration. A European-style option can only be exercised at expiration itself. That single rule is the entire difference.

What trades as which

Most single-stock and ETF options - including options on SPY, the SPDR S&P 500 ETF - are American-style. Index options (like those on the S&P 500 index itself, SPX) are typically European-style and cash-settled. That distinction matters when you choose which product to trade.

Why it matters for sellers

For option assignment, style is everything. A seller of American options can be assigned early - any day the holder chooses to exercise, often around dividends or when an option is deep in the money. A seller of European options can only be assigned at expiration, which removes the early-assignment surprise entirely.

Buyers barely notice the difference. Sellers should never ignore it.

For the option buyer

If you buy options and close them for cash before expiry, the practical impact is small - you rarely exercise either style. The nuance to remember: American options carry a sliver of extra value because the right to exercise early has worth, and cash-settled European index options remove the hassle of shares changing hands. Know which one you are holding, and the rest follows.