Your confusion is understandable, the terms are oft erronously used interchangeable.
A calcium reactor uses Calcium carbonate as a media. CO2 is inserted into the water to make the water acidic so as to disolve the calcium carbonate.
Kalkwasser is Calcium Hydroxide mixed with water and while people often talk about Kalk reactors they are really just automatic stirrers as desribed originally by Alf Nielson. Alf's version used a little moter to stir the kalk periodically but new versions use small pumps. As a cheap alternative some people just stir it or shake it themselves every few days and just have a drip into a refugium or into auto top off water. Alf discovered that freshly stirred kalk was much more stable than kalk allowed to sit idle for too long.
Some people just mix kalk into the auto top off water. The cheapest cheapskates like me just add it or commercial calcium products when we manual replenish evaporated water. Kalk should be added very slowly to prevent massive ph changes because kalk PH is really high.
To add to the confusion Alf also describe using CO2 with kalk to control the ph but that's not required to get the calcium into the water. With a calcium reactor CO2 is required to make the water acidic enough to disolve the calcium carbonate.
I should also mention that the common belief is that Kalk is great for tyipical needs but Calcium reactors can provide alot more calcium for extreme calcium needs.
The general guidance on this is that if you have a tank slam full of hard corals that consume mass quantities of calcium then you will probably be running a calcium reactor. kalk on the other hand can generally supply the needs of most tanks.
The complexity of running a calcium reactor is very high where kalk reactors are fairly straight forward and alot more forgiving.
So with a 150 gallon tank, with several corals already, sounds like I need a Calcium Reactor for sure? So how does one set one of those up and is there a particular model that works better than others? Help me out here guys.
I wouldn't say that at all... A few corals is not "slam full of corals". I think Brandon's suggestion to you is totally appropriate but there is no huge rush. Start with a Nielson reactor or kalk top off if you want but take your time and learn first becase you can manage it easily with bottled supplements until you decide what's best for your needs. Your best tool is patience in reef tanks. Ironman's awesome 150 gal tank has no calcium reactor or kalk reactor. He's just mixing calcium supplement in his water that auto tops off the evaporated water and he has great corals. It's a jug of water with a few squeezes of off the shelf calcium supplement that refills the tank as water evaporates. Actually I think Ironman doesn't even go that far, he pours some supplement right in the tank periodically and his autorefill is plain water.
Very few of the beutiful reef tanks around here use a calcium reactor OR automatic kalk system. My 65 which actually has about 80 gals doesn't have either and it is doing great. You can easily get by with a manual system for awhile just by adding the supplement when you replenish the evaporated water. What I would advise more is let your tank get cycled good for awhile before doing anything drastic. We'll talk about it in more detail this evening when I meet you.