Not necessarily. The internet speed is fastest when the device is directly connected to an Ethernet cable. The speed may drop when connected through Wi-Fi due to wireless interference or due to incorrect router.
The suitable Wi-fi router depends on the internet speed that your plan entitles you to:
Connect your device to any of the router LAN ports and browse, if your device is not capable of connecting to the router through a wire, try to stay close to the router to get better speed.
This could be due to interference from other routers in the premises or any other wireless device which works in the same frequency or bandwidth. Try to avoid placing devices like cordless phones, microwave ovens and other routers near your router. Switch off Bluetooth on your phone. Try to place the router at a good height; the router must have a line-of-sight (LOS) to all other devices in the premises as far as possible.
Install the Wifi Analyzer app for Android devices from the Google Play Store and choose any channel that is free in the premises. If there are no free channels, choose the channel where there is no overlap of SSIDs between 2 channels as shown below.
If the router is a dual band router, try using the 5 GHz channel where there will be less overlap and better speed.
Try making the following changes