Custom dress shirts, or bespoke, as the English say, are shirts made from an individual pattern for the specific customer according to his specific measurements and style requirements. This is very different from made-to-measure, which is accomplished by simply altering a stock pattern or stock pattern pieces to a customer's measurements. In this method, the result can be very inconsistent.
Each time you order true custom shirts, your own paper pattern is used to cut the cloth. Consequently, each time you order, the result will be the same. Our pattern/shirt maker George Bijimenian says "You can only acquire fit with true custom using a paper pattern." In order to buy custom shirts, you can simply check out this link.
When you order made-to-measure, you will have someone translate your measurements and alter the stock pattern.
Since there is no individual pattern on file for you, there is no way to ensure that the alterations to the pattern will come out the same each time. You can get different results depending on who does the translation and measuring.
Made-to-measure almost always works well for the customer who is a standard size and does not require unusual styling. The customer who has a fit problem or very different styling requirements will do much better with custom.
Since not all shirt makers define their terms the same, make sure you know what you're getting when you order "custom dress shirts". Ask the tailor if he makes a full paper pattern from scratch, and be sure the final sample is exactly what you want before approving it.