To add... When you say internet, its a wide area network(WAN). Ie., Its the network from your device going to the server of google in hongkong or to the servers of all domains connected somewhere else-the internet. So internet speed is mostly dependent on your carrier/isp/subscribed speed..

When you say LAN(local area network) speed, its the transmission speed within your device and the router(wireless b/g/n/ax; wired ethernet, fast ethernet, gigabit ethernet). Thats why your router has two interfaces the WAN side(going to the telco) and the LAN side going to your home ntwork. Internet bottleneck often occurs on the WAN, while WiFi signal is the LAN physical medium not related to the WAN.