Direct answer
When you test a VPN while diagnosing or configuring a connection, “problems” are the concrete failures or unexpected behaviors you encounter, and “verification” is the set of checks you use to confirm whether the VPN is working as intended for your specific setup. Because VPN behavior depends on operating conditions, you verify step-by-step and compare results before/after the change.
How it works (problems vs. verification)
Problems typically show up in one of a few areas: the tunnel may not establish, traffic may bypass the VPN due to routing or DNS settings, name resolution may fail or appear inconsistent, or performance may change noticeably. Verification then focuses on confirming the most relevant outcomes for your goal (for example, that traffic is going through the tunnel, that DNS resolution works, and that the client reports the expected connection state).
A useful way to structure your testing is to separate (1) whether the VPN connects, (2) whether it routes and resolves traffic correctly, and (3) whether observed behavior matches your expectations for the selected network path. Each area can fail independently.
Practical context for troubleshooting and setup
Start with stable baselines: record what works before enabling the VPN (for example, general connectivity and DNS behavior). After you connect, check that the same actions behave as expected through the VPN client. If something breaks, test narrowly by changing one variable at a time—such as the protocol choice, the destination network, or location/server selection—so you can tell which change improves the outcome.
Limitations you should account for
A VPN does not guarantee anonymity, safety, or access, and it cannot remove all uncertainty in network behavior. Performance and availability can vary by network, device, location, time, and remote endpoint conditions. Also, some “proof” style checks can produce misleading results if the test website, DNS cache, or local firewall behavior changes after reconnecting.
Because the reliability of any specific claim about a particular product’s current capabilities can’t be assumed from general guidance, treat verification as part of your own measurement process.