Saving the password in your browser is using a password manager; you're just using the one built into your browser. The safety and security of using any individual password manager is pretty much up to how secure that particular password manager is, but generally speaking they all store passwords encrypted.
Ones built into a browser have the added attack vector of being potentially vulnerable from the browser itself vs a stand alone manager, but if you use a plugin for your favorite password manager they likely share a pretty similar attack vector possibility.
Either way, using a password manager is infinitely better than reusing passwords, so this is really just a long winded way of saying "no, not really".
Dedicated password managers usually come with more security, control, and features, but you're generally going to be fine using the one built into your browser.
password managers in the browser still store them encrypted. They usually authenticate via a passkey, in-built security in the OS like windows hello, or through other services such as SSO through google; That said, if you have them on auto-pilot with this authentication, anyone with access to the device can theoretically access them, though to actually view them in the password manager they usually require you to authenticate.
Browser password managers are sorta less secure than a third party one, assuming you turn on all the convenience features to make your life easier, but a lot of third-party password managers have the same convenience features a lot of the time anyways.