The algorithm used on the Speedtest.net website and the Speedtest.net app are very similar, so the difference in speeds is probably due to one of these outside factors:

• Differences in available bandwidth: Make sure that the tests don't overlap each other, as each test needs to have your entire bandwidth to itself. Additionally, make sure nothing else is downloading at the same time.
• Differences in connection: Make sure the phone and your computer are actually testing on the same connection. You may have Wi-Fi turned off, and accidentally be testing your cellular speeds instead.
• Differences in hardware: If you're both on a Wi-Fi connection, know that phones and tablets typically have less sophisticated Wi-Fi antennae than larger devices like laptops. This difference may negatively impact your phone's Wi-Fi speed, especially in areas of high interference on the 2.4 Ghz Wi-fi frequency.