Foreign Equity options are options in which the underlying asset is a foreign equity.
Equity linked foreign exchange options
Equity linked foreign exchange options (sometime know as ELF-X options) are a combination of a currency option and an equity forward contract. If the exchange rate should work in the investor's favour under the option contract, then the total payout from the option is dependent upon the performance of the equities underlying the contract. Otherwise, the investor does not receive a payout.
Quanto Options
Quanto options (or cross-currency derivatives) are cash options that have an underlying asset denominated in a "foreign" currency, but settle in a the "domestic" currency at a fixed exchange rate.
Resolution supports the valuation of both quantos and equity linked fx options as part of the Resolution Exotics module.