How is it possible for a hotel to have Wifi but no internet access?

I think that the websites are confusing terms. I have also seen this on AirBnb where places have separate checks for WiFi and Internet. I think that what they actually mean is:

1. WiFi - non-wired internet access
2. Internet - Wired internet access

As someone who deals with computers on a daily basis for work, these types of bad definitions annoy the hell out of me.

I actually know of a hotel, which has free WiFi but charges for Internet access. Through the free WiFi, you can access the hotel's internal entertainment system, order room service, check out, "call" the front desk, etc. But if you want to connect to the Internet, you have to pay an extra fee (which you can also book through the free WiFi).

As soon as you have confirmed the booking, your MAC address gets unblocked in the router, and you have full access. You also get a keycode with which you can unlock up to 2 other device's MAC addresses.

So, this particular hotel would indeed have Free WiFi but no Free Internet.

Interestingly, I even know of a hotel, which has free WWW access, but you have to pay for Internet access.

I can only speak for hostelworld.com which I use a lot, the difference there is pretty clear to me:

Free WiFi

This means Wireless LAN is available in the facility, but not necessarily everywhere. Often it's just in the lobby but not in the/all rooms. The WLAN is connected to the public internet, so if the guest has a device supporting WiFi, she can use it to go online. This is free of charge. This is very common now.

Free Internet Access

This means there are desktop computers available (running Windows, or sometimes Linux or even MacOS) which can be used by the guests free of charge. These PCs are connected to the public internet. Often there is a time limit on the usage if someone else is waiting. This used to be very common in hostels but newer places often don't bother anymore because everybody has a mobile device with WiFi.

I would consider both statements insufficient for what I usually want, which is generally connecting a personal laptop to the internet.

Some hotels advertise «Free WiFi internet access», yet getting to the internet from the room requires an extra charge (usually disproportionate and daily). You need to look at the fine print which says that restricts that offer to «the common areas»

Internet access may simply mean that there are some computers available for you to use. These computers may be severely constrained (eg. kiosk mode), be running very outdated software, be infected with credential-stealing malware… So I wouldn't recommend using them but for very light tasks (eg. looking up the opening times of a museum)

Thus, when searching with a hotel aggregator those fields would be useful hints, but I would then go to the actual hotel website and check what they claim there to have available. Call them to clarify if needed.