The raised ink is done by a process called thermography. A chemically reactive powder is sprayed on the press sheets while the cards are still wet, then they’re heated, which causes the ink to bubble up and raise. You can get letterhead and envelopes printed this way, but they have to be done with a different precedure or else the ink will melt and gum up as it’s re-heated by your laser printer.
Thermography was invented to mimic the much more expensive process of engraving. For engraving, a plate has to be made (because of the cost, usually of just two cards per press sheet), that’s then used to pusht the ink into the surface of the cardstock.
Other nifty tricks are cards made with custom cutting dies that are stamped into unusual shapes. Or, using translucent vellum carstock, the stock can be made with watermarks in it. Then there’s blind intaglio, where die stamps out shapes in the cardstock like low-relief sculptures.
Gold (or other metalic foil) leafing also requires a custom die. Printing or foil-stamping can be done to register it with the raised intaglio.
Realtor cards are done using photographic printing, becasue they’re done by the bajillion with herds of realtor’s photos on huge press sheets. This volume is how it’s economical. Speaking of economy, most fancy cards are done as “shells,” or “masters” with the main fancy stuff on no-name cards, which are then imprinted individually as people are hired, promoted or run out of cards. If you want fancy cards to hand out, you’d have to pay hefty prices for all these set-ups.
Which reminds me of the cards I printed for the newly-founded Dept of Homeland Security. Most inks are coded into the PMS (Pantone Matching System), with basic colors having a three-digit code. Homeland Security wanted a five-color card shells with each color having 4 or 5-digit codes (custom-mixed, not to be found straight out of the can). Because they chose such distinctive colors, we couldn’t “build” the colors using 4-color process like in most color printing. And then, the imprints for individual employess were to be done in two multi-digit inks. Was it because they wanted Al Qaida to go bankrupt making conterfeit cards? Or egotistical government boondoggle?