What kind of bike should I be looking for? Until recently I thought only weird types had bikes that weren't mountain bikes

I'm definitely interested in this lighter, faster, less energy required bike!
There are a range of road bikes
1) Tough commuter bike. MTB wheels, steel frame & forks. Mudguards. Kona Smoke. Slow and heavy, but will take abuse.
http://www.konabikes.co.uk/2k6bikes/smoke_2k6.php
2) Urban MTB. Just have a MTB but swap the knobblies for road tyres. Best to choose rigid frame.
http://www.cannondale.com/bikes/04/ce/model-4MRBB.html
3) Flat Bar Road Bike. Exactly the same as a drop bar bike, but bar, shifters and brake levers changed to MTB style parts.
http://www.giant-bicycles.com/en-GB/bikes/road/1400/28829/
4) Drop Bar Road Bike. Most commonly used by on road dedicated cyclists, but they have a few drawbacks which others expand on. Drop bars and higher gearing compared to MTB
http://www.giant-bicycles.com/en-GB/bikes/road/1395/29624/
4.5) Modern variant now is with a shorter top tube so you're not so crouched
http://www.giant-bicycles.com/en-GB/bikes/road/1399/29640/
5) Cyclo-Cross. A offspring from a MTB daddy and road bike mummy
http://www.giant-bicycles.com/en-GB/bikes/road/1397/29632/
Usually tougher wheels & hubs, frame, and MTB gearing. Brake levers on the flats (road bikes do not have these, well they did years ago called suicide levers) You can use Cylco-Cross on road, if fact a good idea since you have brakes on both the hoods and the flats, so safer inner-city. Just replace the tyres.
6) Tourer. Available in flat bar or drop bar, with either 26" or 700cc wheels. Usually a shorter top tube, and upward pointing head stem. 700cc & drop bars with front roadie chainset, larger rear sproect classed as "fast tourer" 26" & flat bars MT front chainset more off-road tourer, basically solid framed MTB with panniers. Also some tourers have end shifters
http://www.dawescycles.com/dawes/galaxy.htm
http://www.dawescycles.com/dawes/kara-kum.htm
http://sunnypowers.perso.cegetel.net/pat/ilpompino/bars_sm.JPG
7) Audax, Somewhere between a road bike and a tourer
http://www.dawescycles.com/dawes/audax.htm
8) Hub gearing, ala Raleigh style.

8 gears, low maintenece. Also drum brakes
http://www.giant-bicycles.com/en-GB/bikes/lifestyle/2137/31763/
9) City bike, similar to a hybrid but solid forks. Usually raised stem & bars, like the old style dutch bikes. More upright than MTB, short top tubes.
http://www.giant-bicycles.com/en-GB/bikes/lifestyle/2139/31774/
10) Folding. After use fold up and put under your desk. Usually expensive, starting at £500. Checkout Brompton
http://www.giant-bicycles.com/en-GB/bikes/lifestyle/175/31785/
11) Time Trial. Usually a souped up road bike, with aero bars, carbon everything
http://www.giant-bicycles.com/en-GB/bikes/road/1396/29626/
12) Track bike. Stripped down road bike, no brakes, single speed. Not a good idea to riding in Buxton
http://www.witcombcycles.co.uk/images/track2.jpg
Then you have the components (wheelset, gear & brakes, chainset, dereailers)
http://www.campagnolo.com/jsp/en/index/home_true.jsp
http://www.shimano.com/
http://www.sram.com/
Then different materials used for frames, steel, cro-mo, alminumium, carbon, titanium. Also mixtures, ie alu frame + carbon fork, alu frame with carbon rear stay etc. And classic style steel frame
http://www.condorcycles.com/classico.html
One thing to check if you want a road bike & full length guards is the gap between tyre and underside of the brake arms. Most road bike won't take guards but some have long reach brake arms. You should be able to pass your finger between the two. Also check for guard mount holes. If you ask for a road bike with full length guards they'll direct you to a right one.
So as you can see there is no right bike I can say which fits you, you have to work that out yourself, there are just too many variables. Nothing is stopping you using a fast tourer for work, likewise you can use a road bike for work also. You might not like drop bars in traffic you need to be on the hoods. Also road bikes are quite crouched position, if you have a bad back you might find it uncomfortable. Or you might prefer the totally upright position of a City bike. Or if you're a aggressive cyclist kerb hopping then you'll need a urban MTB not a road bike as the wheels wouldn't last that long.
These are my two bikes.
Orbit Helium (company now bust)

Steel fast tourer, with Campagnolo Veloce groupset. Brooks 17 saddle
Giant OCR-1. Alu frame, carbon fork. Campagnolo Mirage groupset. Brooks Team Pro saddle