There are two related issues here.
First, emoji are just text, and the appearance of all text depends on the system font of the device they’re being viewed on (when the website doesn’t specify a font, or the specified font does not exist on the device).
So even if you were to see the “Apple version” on your computer, your users would see a different version depending on their own devices’ system font.
The only way to ensure consistent “Apple emoji” for ALL users is to ship the Apple emoji font with your website, perhaps through your theme, just as your theme may come with some custom font that all users see.
But this does not explain why you don’t see the “Apple” emoji on your own device, which clearly should support the Apple emoji font (because that’s where you entered it from) ??
That’s where the second issue comes into play.
To ensure consistent display of emoji on all devices, including devices that may not even have the emoji font at all… WordPress does two things:
1) WordPress uses Twitter’s version of emoji, called Twemoji. This ensures consistent display on all devices, just as your site text is (most likely) shown with the same font on all devices.
2) WordPress also serves the emoji (ie Twemoji) as images, rather than text characters. This ensures the emoji can be seen on ALL devices, including devices that don’t support emoji at all. (This explains why you briefly see the Apple design — which is the text emoji served as the alt
text for the image — before the Twemoji design, which is served as an image.)
… and it automatically changes from the Apple version to the Android version,
It’s not the “Android version” per se, but the Twemoji version. Some of the Twemoji characters may be similar to Android’s emoji, some may be similar to Apple’s emoji, some may be similar to Windows emoji, some may even be the official Unicode emoji characters… but, collectively, it’s all Twemoji. See all the Twemoji characters here: https://emojipedia.org/twitter/