Some info --
Tech diving involves deeper diving (usually deeper than 100 feet), alternative gases (vs. air), overhead environments (wreck or cave penetration diving), redundancy (given the riskiness of these dives, tech divers have to carry multiple gas systems -- most often double tanks -- and other redundant gear). Their dives also typically involve decompression stops -- meaning that they exceed "no decompression limits" and then have to follow a very specific schedule of decompression stops at various depths for various times. Most of their deco time is spent hanging in the 15-20 foot range, since it is the last 30 feet of depth below the surface where the human body experiences the most decompression. For deeper divers for extended periods, it is common for tech divers to spend more time decompressing at 15-20 feet than at the bottom.
DIR -- "doing it right", is a diving philopsophy that has been developed by technical cave penetration divers. As mentioned above, this type of diving involves added risk. The DIR philosophy involves gear standardization, attention to physical fitness, gas management and a strict adherence to the buddy system in order to minimize these risks.
DIR has started to make its way into the recreational diving community, since many divers feel that it can provide an additional measure of safety to all divers. This tends to be a controversial topic, for various reasons. Some staunch DIR advocates feel that if you aren't "DIR" than you are an unsafe diver. Other divers see benefit to some but not all of the DIR techniques and recommendations (viewed as heresy by the "all or nothing" DIR types). Others condemn it as a marketing ploy to sell certain types of gear. There are folks on this board who fall into all three of these camps. Many folks have used a religion analogy to describe DIR -- you have the zealots, the casual church attenders and the agnostics -- each has different reactions to the religion and it affects their daily lifes (or diving) in different ways.
Do a search on this site using the word "DIR" and you'll find a couple of "DIR primer"-type threads that will get you started.
One other idea regarding terminology -- there is a "buying your first gear" article in the August edition of Rodale's Scuba Diving. This article has a glossary of terms that you might find useful. I think it is similar to the link below. Newdiver.com is affiliated with Rodales and scubadiving.com.
http://www.newdiver.com/gear/divespeak.shtml
Good luck!