The main difference is responsibility
Shared web hosting usually provides a managed environment designed for common website software. A VPS gives a customer an operating system with more control. More control also means more responsibility for updates, access, firewall rules, and recovery.
Look at the application first
If your site fits a standard platform and you do not need server-level settings, shared hosting may be enough. If you need custom daemons, system packages, or unusual runtime configuration, a VPS may be worth evaluating.
Consider the operating burden
A VPS requires someone to patch it, monitor it, keep backups, troubleshoot services, and respond to security problems. A management add-on may alter this boundary, but only a clear written scope can establish what it covers.
Move when a constraint is measurable
Use logs and resource data to identify the limit you are hitting. Do not upgrade based on vague expectations. Compare the actual shared plan limits with a VPS configuration and account for administration time.