A recorder with nothing behind it
Most online voice recorders upload what you say to a server, either to process it or simply because that is how the site was built. This one does not have a server in the path at all: the browser captures the microphone, its built-in encoder writes the file, and the file lands in your downloads folder. You could disconnect from the network after the page loads and it would work exactly the same.
That matters more for audio than for most things. A voice memo is often the most personal file someone will make all week.
Getting a clean recording
The single biggest improvement is distance: a microphone thirty centimetres from your mouth sounds dramatically better than one a metre away, because the ratio of your voice to the room goes up. A headset or earbuds with a mic will beat a laptop's built-in array almost every time.
After that it is the room. Soft furnishings absorb reflections; bare walls and hard floors create the echo that makes recordings sound hollow. Echo cancellation and noise suppression are enabled here and help with steady background noise like a fan, but neither can undo a reverberant room.
Why the format differs between browsers
The recording is encoded by the browser itself, and browsers ship different encoders. Chrome, Edge and Firefox produce WebM containing Opus — a modern codec that sounds notably better than MP3 at the same size and is particularly good at speech. Safari produces M4A. If something downstream insists on MP3, convert it afterwards; there is no benefit to recording in it.
Download before closing the tab
The recording lives only in this page's memory until you save it. There is no draft, no autosave and no copy on a server, because there is no server. Reloading the tab loses it.