How does product management differ when you are working to create a custom infrastructure platform?

"Custom infrastructure platform" is nearly an oxymoron. :-) Anyway, it doesn't sound like a product; products are offered for sale to a market.

A "custom infrastructure platform" is very likely an internal project. It will have organizational stakeholders, clearly defined objectives (be very cautious here!), and a budget based on a (likely inflated) forecasted operating outcome. A project or program manager will be responsible for delivery here, and they partner closely with a technical architect who designs the system to spec. 

While there are certainly aspects of project management overlapping with product management, it is a distinct discipline worthy of its own AMA!