Around the office, we might like an instance of tea, but we vehemently oppose instant tea.

That's because instance means an example or an occurrence:

Police investigated five instances of criminal mischief to motor vehicles on Forest Avenue

A student in the engineering academy, for instance, would have to take three engineering-specific electives.

There was an instance in a game in August where the catwalk came into play.

Instant, on the other hand, mean immediately or urgently:

Easy Reader: Philip Roth's Nemesis an Instant Classic

Starbucks announced last summer it would start retailing flavored instant coffee, and here it is.

Now think about the times when you fell victim to the instant desire to buy that new shinny thing.

Oddly enough, the two are related. Instance dates back to 1380 as meaning the current time, but it comes from the Medieval Latin (through Old French) instantia, which refers to both presence and urgency. Instant dates to about the same time, prior to 1398, as meaning a specific moment. It comes from the Medieval Latin instantem, meaning present and urgent. Instant picked up its modern meaning of immediately around 1443 from its English definition and instance seems to have never meant urgency, creating a distinction between the two.

But instant tea is still disgusting.