No. While both accounts can be used for qualified medical expenses, there are significant differences. A Flexible Spending Account (FSA) is fundamentally different than a Health Savings Account (HSA) for two main reasons.
An FSA is “use it or lose it”, meaning if you don’t use the money in it, you will lose the ability to use it later (subject to limited carry forwards and a grace period). The FSA account is also not yours, it is your employer’s. Additionally, you have to make an election at the beginning of each Plan Year to determine how much money you want to put away. An FSA, however can be used with almost any type of health insurance (low or high deductible) while the HSA is only applicable with a High Deductible Health Plan (HDHP).
An HSA on the other hand has significant advantages. It is your account and your money and it is portable. Meaning if you decide to leave your employer, you can take all of the money in your account with you. You can also rollover your balances year-to-year. The contribution limits are also higher with an HSA vs. an FSA.
Source:IRC Sec. 223(d)(1)(E)