A countertop system is mostly used by people who do not want to mess with the plumbing -- for example, renters of apartments and offices or homeowners who intend to move soon.
Reverse Osmosis systems purify water so slowly that they normally come with a tank. As a result, the system can be trickling water out 24 hours a day (if necessary) so you can wake up with a full tank of purified water every morning.
On the other hand, a countertop system does not come with a tank, so you have to be patient while the water trickles out to fill up your glass. One way around this is to fill up a 2 or 3 gallon jug of water so when you or a member of your family wants a glass of water, it's already waiting in the jug. We sell 2 gallon jugs with a spigot for $10.
There is a lever on the connection to the faucet so you can have regular tap water or R.O. water.