that's most likely because the Wi-Fi chip in the laptop is cheap or is older tech and doesn't support up to 100mbs over Wi-Fi.
60mbs average is typically what you get for most any 802.11g/n Wi-Fi connection on a 2.4Ghz band.
You want faster Wi-Fi you're going to need to get a USB Wi-Fi adapter with support for wireless AC connectivity (also assuming your router supports AC as well.) The only way to get faster on your laptop is if the Wi-Fi chip inside supports connecting to a 5Ghz network (and assuming your router supports broadcasting in 5Ghz) but at that point, you'll need to be a bit closer to the router since the 5Ghz band gives greater speeds over wireless at the cost of range.
Doing a speedtest with a laptop on Wi-Fi will only show you what speed your laptop is getting. It has no bearing on what your ISP is providing you through your modem. You are paying for 100mbs. And you are most likely getting that. But your laptop isn't capable of getting those speeds itself when on Wi-Fi. Connect the laptop to the router using an ethernet cable and you'll see you're getting closer to the 100mbs.
You can get after-market wireless cards, but you'll need to check if it's two or three antenna wires. It may or may not work, but you can get an 802.11ac card fairly cheap on Amazon.com or whatnot. The easiest option is just to get an 802.11ac USB dongle; install drivers and plug it in. In addition, you're router that supplies WiFi will need to be in the 5Ghz band to reach higher speeds.