What is the difference between wi-fi and wi-fi cellular in purchasing an i-pad?

A WiFi only iPad will only connect to a WiFi hotspot. The WiFi Cellular model will connect using a cellular connection provided you sign up for a cellular data plan for it. In short a WiFi only iPad won't connect to the internet if you are not within range of a WiFi network you can connect. The WiFi/cellular model will connect anywhere you can get a cellular connection, but will cost you for a cellular data connection.

The cellular models allow you to use a cellular network to access the internet when you don't have access to a wifi network - on an iPad it only gives you data access over the network of your chosen carrier (email, browsing etc), it doesn't allow you to make 'normal' phone calls.

The cellular iPads also have a built-in GPS chip which the wifi-only models don't have, so some people get it for that and never take out a cellular contract with a carrier.

One has cellular the other doesn't.

The Cellular or 3G portion allows an iPad to connect to the internet using a Cellular network like the one a regular Cell phone uses. So you have internet anywhere you are without requiring a Wifi network to connect to.

Cellular iPads require a Data Plan from a Cell Carrier to use their Cellular portion. However their Wifi portion works just like al Wifi only iPad and does not require any additional plan. If you have Wifi at home it can connect to that at no additional cost to you.

You'll need to check with your cell carrier whether they have data plans for iPads. And if you are willing to pay for the extra service.