Different front and rear tires

Depends - the rear in the old style parings you mentioned is designed for drive traction with the paddle centre tread, the fronts for steering and cornering. That's a generalisation as not everyone will like a particular tyre profile and nor will they necessarily work in all sorts of terrains. So, a "pair" of tyres might not necessarily be for you.

For example, I like the rear Velociraptor but don't like the way the front one corners.

There are rounder profile tyres and tyre sets, and squarer or "edging" profile tyres. Tyres with directional treads for either end, tyres with non directional treads.

And of course there are different sized tyres - typically many riders use a wider tyre up front for more steering and braking control with a narrower tyre out the back that's easier to pedal.

Your LBS and other local riders will have some idea what works for your bike, terrain and style of riding - this can be a good place to start.

Or, tell us what bike you have, how you want to ride and we can take a stab at what might suit.

I am currently riding a Raleigh hardtail, which limits my desired riding style to pretty much just riding the thing. I did upgrade the wheel set to Sun Rhinolytes, but the bike is entry level and as such not good for much of anything. In the near future I hope to have a full suspension, which would permit me to do some light downhill/freeride and small jumps/drops. Whichever tires I purchase, I would like to be able to transfer to the new bike should they be needed. Where I live (Victoria, TX) there is not much in the way of options. There is one decent lake trail with some good tree runs and a few good hills and a bmx track. All of which is hardpack with loose sand and loam. However, there are cities within 100 miles (Austin, San Antonio, etc) that have a multitude of trails for all styles and levels of riding. Austin trails are most likely very rocky whereas San Antonio is probably hard clay and rock. As far as the LBS goes, I will not go there nor will I ask their advise on anything. They burned that bridge. Other riders? Aside from my friend and I (both newbies), I haven't seen any .