Wi-Fi and wireless are the same things in that they both allow devices to connect to the Internet without a cable. The result is the same; however, the difference is in the method of connectivity. Wi-Fi is a wireless networking technology that permits smartphones, computers, laptops, and other devices to connect to the Internet or speak with each other wirelessly. The Internet is a global network of connecting networks that links millions of computers globally using cables, telephones, lines, satellites, or wireless connections. Wi-Fi uses radio waves to transmit and accept signals from nearby devices to provide internet access.
The Internet allows you to access data or information from across the world, while Wi-Fi devices must be fully equipped with wireless network adapters to join a wireless network. Wireless connects to Wi-Fi, but not necessarily the Internet. The Internet does not require Wi-Fi to connect.