Deionized and distilled are essentially the same, assuming both are good quality. Sort of different means to the same end.

Distilled water is made via distillation (duh), and Deionized is made via filtration. The end goal of both is to remove particulates from the water. Particulates can be ions ("sticky" atoms missing an electron), neutrally charged atoms, or colliods (neutral charged atomic clusters).

The problem is that when buying store-bought distilled water, you don't really know what you are getting. µS (microsiemens) is a measurement of conductivity. Proper quality distilled water should measure below 2µS. Most DI water will range somewhere between 0.5-5µS depending on the quality level the system is designed to provide.

In general, a high quality distilled water will be purer than average DI water, but this is not always the case. A person I spoke to about a product I am currently working on, said that he personally has measured store bought distilled water as high as 86µS (this is BAD quality distilled water). He contacted the manufacturer of the water and warned them that they were having a problem with their system, and a few weeks later he tested their water @ 25µS. He called once more, and on the next batch the purity was finally down to a reasonable spec of 3µS.

The only way to really guarantee the purity of the water you are using, regardless of what it says on the bottle, is to buy a TDS (total dissolved solids) meter and measure its conductivity yourself. For those of you in school your chem lab may have one you can use.