please elucidate what goes into the "custom" solution after you have a prototype with an arduino?
A custom-designed PCB that includes all the relevant parts of the arduino (which can vary depending on what your product does), plus whatever additional components your product uses. Designed with careful attention to type and placement of connectors to off-board components, eliminating them as much as possible. (no matter what else, connectors are ALWAYS a weakness when it comes to hardening a product.)
I wouldn't feel too bad about an actual arduino/shield combination; those connectors "match" and by the time you get 28 pins worth it's pretty sturdy. But the common prototyping practice of sticking in rather arbitrary wires into the arduino connectors would be insane...
"Manufacturing Engineering" is a whole separate discipline from EE or CS. There are experts, and consultants. They're expensive. (And not everyone does a good job. There are lots of crappy products out there.)
The details, and exactly who or what you should employ/study, would depend pretty strongly on exactly what you're trying to do and in what environment. Which you haven't told us. Some industries have STANDARDS for stuff (which gets you from manufacturing engineering to compliance engineering. and test engineering.) UL, CSA, CE, FIPS, NEBS, MIL-Spec, NASA, and many many more.
Sometimes it's a wonder that there are any commercial products at all.