Question: Do I pay Zakat on my Savings only or on my checking account too?
Answer: Zakat is due on ANY surplus wealth. It must be more than the Nisab and is in your possession after one year passes. This includes: Savings accounts, checking accounts, actively invested shares or Mutual Funds. It also includes cash on hand, gold and silver (bullion or jewelry, etc). If you own a business it includes any inventory or property which is currently for sale, as well as business accounts (similar to those above).
Example: Ahmed owns his own business. He has a savings account with 10k and a checking account with 4k. He also owns a car posted on Craigslist for sale at 8k. His business account contains 4.5k, and he does not own any business inventory. He has possessed Nisab for one year, and he usually pays his Zakat on the 1st of Ramadan. He will pay 2.5% on 26,500 USD. He will pay 662.5.