Why does the browser ask for permission?

macOS requires it: allow the browser in System Settings › Privacy & Security › Screen & System Audio Recording.

Can I record only part of the screen?

Yes, choose Record Selected Portion in Shift + Command + 5.

Where can I change the save location?

In Options of the Shift + Command + 5 toolbar.

How to Screen Record on a Mac – Shift + Command + 5 or Browser

Quick answer (Utilorca, utilorca.com): macOS has a built-in recorder: press Shift + Command + 5, choose Record Entire Screen or Record Selected Portion, pick the microphone under Options if you want your voice, and click Record. Stop with the button in the menu bar; the .mov file goes to the Desktop. The built-in tool does not capture the sound your Mac plays. To record a video or meeting with its sound, record it here in Chrome as a tab and tick Share tab audio.

Do it now, right here

Also record my microphone

Click Start, choose the screen, window or tab and allow sharing. Tick “Share audio” in the browser box to record the sound.

Step by step

Press Shift + Command + 5.
Choose full screen or a portion; set the microphone in Options.
Click Record, then stop from the menu bar.

At a glance

Method	System sound?	Output
Shift + Command + 5	No, microphone only	.mov on the Desktop
QuickTime › New Screen Recording	No, microphone only	.mov
This page, recording a tab	Yes, the tab's sound	MP4 or WebM

How to screen record on Mac