What is the difference between UTF-8 and Unicode?

Let me use an example to illustrate this topic:

A Chinese character:      汉
its Unicode value:        U+6C49
convert 6C49 to binary:   01101100 01001001

Nothing magical so far, it's very simple. Now, let's say we decide to store this character on our hard drive. To do that, we need to store the character in binary format. We can simply store it as is '01101100 01001001'. Done!

But wait a minute, is '01101100 01001001' one character or two characters? You knew this is one character because I told you, but when a computer reads it, it has no idea. So we need some sort of encoding to tell the computer to treat it as one.

This is where the rules of UTF-8 come in: https://www.fileformat.info/info/unicode/utf8.htm

Binary format of bytes in sequence

1st Byte    2nd Byte    3rd Byte    4th Byte    Number of Free Bits   Maximum Expressible Unicode Value
0xxxxxxx                                                7             007F hex (127)
110xxxxx    10xxxxxx                                (5+6)=11          07FF hex (2047)
1110xxxx    10xxxxxx    10xxxxxx                  (4+6+6)=16          FFFF hex (65535)
11110xxx    10xxxxxx    10xxxxxx    10xxxxxx    (3+6+6+6)=21          10FFFF hex (1,114,111)

According to the table above, if we want to store this character using the UTF-8 format, we need to prefix our character with some 'headers'. Our Chinese character is 16 bits long (count the binary value yourself), so we will use the format on row 3 as it provides enough space:

Header  Place holder    Fill in our Binary   Result         
1110    xxxx            0110                 11100110
10      xxxxxx          110001               10110001
10      xxxxxx          001001               10001001

Writing out the result in one line:

11100110 10110001 10001001

This is the UTF-8 binary value of the Chinese character! See for yourself: https://www.fileformat.info/info/unicode/char/6c49/index.htm

Summary

A Chinese character:      汉
its Unicode value:        U+6C49
convert 6C49 to binary:   01101100 01001001
encode 6C49 as UTF-8:     11100110 10110001 10001001

P.S. If you want to learn this topic in Python, click here.

To expand on the answers others have given:

We've got lots of languages with lots of characters that computers should ideally display. Unicode assigns each character a unique number, or code point.

Computers deal with such numbers as bytes... skipping a bit of history here and ignoring memory addressing issues, 8-bit computers would treat an 8-bit byte as the largest numerical unit easily represented on the hardware, 16-bit computers would expand that to two bytes, and so forth.

Old character encodings such as ASCII are from the (pre-) 8-bit era, and try to cram the dominant language in computing at the time, i.e. English, into numbers ranging from 0 to 127 (7 bits). With 26 letters in the alphabet, both in capital and non-capital form, numbers and punctuation signs, that worked pretty well. ASCII got extended by an 8th bit for other, non-English languages, but the additional 128 numbers/code points made available by this expansion would be mapped to different characters depending on the language being displayed. The ISO-8859 standards are the most common forms of this mapping; ISO-8859-1 and ISO-8859-15 (also known as ISO-Latin-1, latin1, and yes there are two different versions of the 8859 ISO standard as well).

But that's not enough when you want to represent characters from more than one language, so cramming all available characters into a single byte just won't work.

There are essentially two different types of encodings: one expands the value range by adding more bits. Examples of these encodings would be UCS2 (2 bytes = 16 bits) and UCS4 (4 bytes = 32 bits). They suffer from inherently the same problem as the ASCII and ISO-8859 standards, as their value range is still limited, even if the limit is vastly higher.

The other type of encoding uses a variable number of bytes per character, and the most commonly known encodings for this are the UTF encodings. All UTF encodings work in roughly the same manner: you choose a unit size, which for UTF-8 is 8 bits, for UTF-16 is 16 bits, and for UTF-32 is 32 bits. The standard then defines a few of these bits as flags: if they're set, then the next unit in a sequence of units is to be considered part of the same character. If they're not set, this unit represents one character fully. Thus the most common (English) characters only occupy one byte in UTF-8 (two in UTF-16, 4 in UTF-32), but other language characters can occupy six bytes or more.

Multi-byte encodings (I should say multi-unit after the above explanation) have the advantage that they are relatively space-efficient, but the downside that operations such as finding substrings, comparisons, etc. all have to decode the characters to unicode code points before such operations can be performed (there are some shortcuts, though).

Both the UCS standards and the UTF standards encode the code points as defined in Unicode. In theory, those encodings could be used to encode any number (within the range the encoding supports) - but of course these encodings were made to encode Unicode code points. And that's your relationship between them.

Windows handles so-called "Unicode" strings as UTF-16 strings, while most UNIXes default to UTF-8 these days. Communications protocols such as HTTP tend to work best with UTF-8, as the unit size in UTF-8 is the same as in ASCII, and most such protocols were designed in the ASCII era. On the other hand, UTF-16 gives the best average space/processing performance when representing all living languages.

The Unicode standard defines fewer code points than can be represented in 32 bits. Thus for all practical purposes, UTF-32 and UCS4 became the same encoding, as you're unlikely to have to deal with multi-unit characters in UTF-32.

Hope that fills in some details.