The Win + . sequence opens the Emoji selector window, which as the name implies can only be used to select emojis. It's also more disruptive since it opens a separate window where you must navigate to or search for the desired emoji, select it, close the window, and then paste the selection into the original app. WinCompose (like XCompose) works as you are typing, without opening a new window; you just type a certain sequence starting with a special Compose key (like "Right-Alt ( 3 )") and it inserts arbitrary pre-defined characters (in this case ③). The key sequences and their replacements can be redefined by the user.
I don't know about everyone else, but in my copy of Windows 10, Win+. opens a small window attached to the text box I'm typing into. I can then type the name of the symbol I'm looking for, hit enter, and the symbol is inserted into the text box. Escape closes the box, so I don't even have to touch my mouse.
Hm. That doesn't look anything like the window I see when I type Win + . while connected to my Windows 10 PC at work. (All my own systems run Linux, so I can't test it locally.) That could be due to version differences, enterprise settings, or the fact that I'm accessing it remotely, but the UI I get behaves as a separate program, not an input method overlay, and only shows emoji.
If you win+. from the carat/focus on text input, just type a hint for the emoji and hit enter (or use arrow keys to select other result) and it should replace the string you typed. i.e. win+. Skull
Interesting. That was not my experience. I could type to search, but pressing enter just showed a message about copying the emoji to the clipboard. This was over a Remote Desktop connection, so perhaps that affected the behavior? Or it might depend on the specific type of text input field.
In any case, most of the characters I use XCompose for (such as arrows, mathematical operators, Greek letters, and non-ASCII punctuation) are not emojis and cannot be selected this way.
This is so nearly awesome, but the hint only works for emoji. So I can type "<WIN>+. sad <ENTER>" for a sad emoji but, e.g., "<WIN>+. gamma" doesn't find the Greek letter. There seems to be no way of selecting a symbol using only the keyboard. So I go back to charmap. Its shitty UI hasn't been improved in decades but at least it can search all of the unicode characters.
Wincompose can handle emojis, Compose compose g o b l i n will give you a tengu ("Japanese goblin") emoji for instance. But it's on you to try to guess what you think their names are and I usually fail.