A production rod would be any that was mass-produced on a larger scale, typically in a factory (though not always), by more than one person (usually several). These rods could be purchased by mail order catalogs, directly from the company, or at retail outlets. The vast majority of bamboo rods are production, made back in the days when bamboo was the primary material for making fishing rods.
A handmade rod is one in which a single person (or very small number of people) is involved in the making of the rod from start to finish. These types of rods are usually much higher in quality & less available on the market. Typically these rods are purchased directly from the maker & would include the custom rod market.
Color of the bamboo: The color of the bamboo in the rod may be darker than a handmade rod. It might also be more uniform in tone. Larger rod companies would look for ways to keep things consistent in the manufacturing process so that the employees could perform the tasks quickly & efficiently. To get the color to the bamboo they would often use chemicals. These chemicals were usually added to the ovens where the bamboo was heat tempered. The only real problem with this was that those chemicals were toxic & the fumes from them could (eventually) be deadly - but they didn't know that back then. Be that as it may, you'll often find production rods a more uniform color throughout the rod.
Node spacing &/or node staggering: In production rods nodes can be all over the place. A handmade rod will have the nodes staggered throughout the length of the rod shaft in such a way that they are as evenly spaced as possible, no two nodes are next to each other in neighboring bamboo strips, & no nodes are found close to either the rod tip tops or the ferrules. Not so in production rods. You can find nodes just about anywhere on the rod, sometime right next to each other. While this is considered a functional no-no in rodmaking, the existence of rods with neighboring nodes fishing for fifty plus years proves this might be more of a cosmetic issue than a structural one. You be the judge.
Varnish: In production rods (especially ones of lesser quality) the varnish was often applied in thicker, fewer coats. This was done to save time. Anyone who's worked with varnish knows that it's much harder to get dust bunnies & other inevitable blemishes out of a thicker coat of varnish (plus it doesn't set up as well). As a result, you can often find some blemishes in cheaper production rod varnish.
Overall fit & finish: The parts on production rod were usually applied pretty well - even on the cheaper grades. This is easy to understand as nothing will send a rod back to the factory from the store or customer than a loose reel seat or wobbly ferrules. However, glue doesn't last forever so if you're shopping for a production rod be sure to check the tightness of things before you buy - if you can.