How Unicode Code Points Work
A code point is a number
Unicode assigns each character a number called a code point. The Latin capital letter A is U+0041, the Greek small letter pi is U+03C0, and the grinning face emoji is U+1F600. The number is the identity; the bytes used to store it can change with the encoding.
The U+ prefix tells you the value is written in hexadecimal, so A-F appear as digits when needed. Padding keeps familiar groups readable: U+0041 has four digits while U+1F600 has five.
From code point to character
When a text system sees a code point, it consults the Unicode standard and the installed fonts to find a matching glyph. The character itself is not physically stored in the code point; the standard says which character the number represents.
In this lookup, entering 1F600, U+1F600, or the emoji itself should resolve to the same record because all three routes reach the same code point.
Example: reading U+1F600
U+1F600 breaks into U+, then the hex value 1F600. Converting 0x1F600 to decimal gives 128512, which is the grinning face. The same character can be copied from this site as an HTML entity, a JavaScript escape, or a UTF-8 byte sequence.
The number never changes between the code point table and the detail page, so you can trust the record even when a font renders the face differently.