Quick answer
Custom software development delivers a defined system to a specification. Product engineering builds and evolves a living product against business outcomes. If your software will have users and a roadmap, you want product engineering.
Goals
Custom software: ship the spec on time and budget. Product engineering: maximize adoption, retention, and revenue over the long term.
Team
Custom software is typically a delivery team. Product engineering is a cross-functional pod with PM, design, engineering, QA, and DevOps.
Process
Custom software is waterfall-leaning with milestones. Product engineering is continuous, data-informed, and release-driven.
When to choose what
Internal tools, integrations, automation: custom software is fine. Customer-facing or revenue-generating products: choose product engineering.