DNS over HTTPS, often called DoH, carries DNS queries inside HTTPS. It protects the transport of those queries between the client and the selected resolver.
What changes in practice
Ordinary DNS lookups can reveal requested domain names to observers along the path. DoH changes how the lookup reaches its resolver. The resolver still receives the question and must be trusted with it.
DoH does not hide every connection detail from a network, change your public IP or make the destination website anonymous. It protects one part of the process of finding a website.
Browser settings can differ from device settings
A browser can select a DoH provider independently of the resolver configured on the device. This helps explain why a browser DNS test may show a different operator from an operating-system settings screen.
Firefox documents configurable DoH protection levels and provider choices. Read the description of the active level, including how it behaves when encrypted DNS is unavailable. An enabled-looking control is not a complete description of every fallback condition.
Check the right result
Use DNS leak testing to observe resolvers handling test lookups. Use DNS lookup to ask Google Public DNS for records for a domain. Those tools answer different questions.
If a workplace depends on internal DNS names, ask its administrator before changing the resolver. For a personal device, record the previous setting and change one layer at a time. That makes it possible to restore normal behavior if a website stops resolving.