I'm new to the hobby, but I know a bit about water treatment thanks to my day job. Here are several fairly concise articles about water purification methods (all fairly well written for wikipedia):
http://en.wikipedia.org/wiki/Purified_water
http://en.wikipedia.org/wiki/Reverse_osmosis
http://en.wikipedia.org/wiki/Distilled_water
Distillation and reverse osmosis are two methods of purifying water, with the resulting product water being similarly low in dissolved solids (i.e. salts, such as calcium or nitrate). That is, the two products are essentially the same. However, distilled water has certain requirements which must be met in order to qualify as 'distilled.' In other words, water can be 'purified' by RO and not qualify as 'distilled.' But again, unless you are performing chemistry, the difference is too slight to worry about. Always mix your seawater according to specifications, and allow time for dissolution of salt and gas exchange.
However, just to scare you with some theoretical points: There can be lingering problems with either method if not performed thoroughly. For example, if carbon is not appropriately used before either RO filtration or distillation, salts will be removed but certain chemicals can survive (e.g. chlorine in RO systems is not removed by the membrane, and chloramines can survive the boiling process in true distillation - either chemical is bad news for our tanks!). Also, most non-municipal RO treatment units do not employ a UV or ozone step, which disinfects the product water of various microbes. That said - there is very little risk that the stuff you buy is improperly purified, and it becomes silly to worry about minor risks. Just be aware. I still like to test my source water before I mix any salt.
/Soapbox
High-quality in-home RO systems include a relatively coarse sediment filtration step, a carbon pre-filter to protect the membrane, the 'RO' membrane itself, and a carbon post-filtration step to further reduce chemical constituents. Without the carbon steps, large-molecule salts might be removed while chemicals like chlorine remain. Don't skimp on quality. Having the RO unit in your home means that you have control over the filter maintenance and eliminates doubt as to whether ALL appropriate steps (carbon, membrane specs, etc.) are included in your system.
/Soapbox off
I hope some folks out there find this useful. If not, forgive my wordiness! =)