What each file is for
favicon.ico holds 16, 32 and 48 pixel versions in one file and works in every browser, old ones included. The PNG favicons give modern browsers a sharp tab icon. apple-touch-icon.png is used when someone adds your site to an iPhone or iPad home screen, and the Android icons plus site.webmanifest are used when your site is installed on Android or as an app.
What is a maskable icon?
Android crops app icons into circles, squircles or rounded squares depending on the phone. A maskable icon fills the whole square with your background colour and keeps the logo inside the middle 80%, so nothing important is cut off whatever shape the phone uses.
Tips for a clear favicon
At 16 pixels, detail disappears. A bold letter, a simple mark or the most recognisable part of your logo works better than the full logo with words. Strong contrast between the mark and the background helps it stand out among other tabs, in both light and dark browser themes.