First the similarities: Both types of lasers are called "diode lasers" or "semiconductor lasers" referring to the main type of materials the make up the light source. The main features of this type of laser are their small size (handy for putting in things like pens and handheld scanners), and their ability to operate off of electrical power from the wall or from a battery. Other kinds of lasers that are not diode lasers need to be "pumped" by another light source to work.

Now for the differences: It's possible that the same exact diode laser can operate in both a laser pen and in a barcode scanner. In this case, they would both be the same color--namely both red. But, if you want a different color for your pen laser, say blue for example, then you need a different diode laser made out of a different semiconducting material. Most red lasers are made from an alloy of AlInGaP, 4 periodic table elements, and most blue laser diodes are made out of alloy of InGaN. The wavelength, or color, of the laser is determined by the elemental composition of the laser material.

The red lasers used in both? Absolutely nothing - they're the same frequency, same laser. The supermarket scanners also have, well, scanners, that watch the reflected laser light, but the lasers are the same.

Note that lasers that aren't that familiar red hue are different (they use different elements and different frequencies). There are of course red lasers that are different as well and are different shades of red, but the common one is the same as far as I know.

The earliest barcode scanners and red laser pens were actually both made using helium-neon gas lasers. In these lasers, a small capillary tube containing a mixture of mostly helium and some neon is excited by an electrical discharge. When the helium atoms get excited and collide with a neon atom, the neon gets excited and radiates light at a wavelength of about 633nm, which is the wavelength of red light.

With improvements in technology, these gas lasers were phased out and replaced with laser diodes. Instead of having a gas as the active medium, laser diodes have a p-n semiconductor junction. Using different materials as the semiconductors results in different bandgaps, which result in different wavelengths of light (i.e. different colors) being emitted. Since it's cheapest to produce laser diodes that emit red light, barcode scanners typically use red laser diodes.