MP3 is a file format. It is a digital object which contains data. That data can be read by a program and interpreted as music, speech, or other sound. Fun! There are many different files which can store sound, each with its own respective parameters, strengths, and weaknesses. MP3 is among the most common because it is compatible with many different programs, it compromises fidelity and quality for speed and size-efficiency, and it is a generalized tool rather than a specific one (meaning it is useful in more places for more people and thus proliferates). MP3s, like many other audio formats, can be put on a CD, whether for storage or playback.

CD is a physical format. It is a physical medium (an optical disc, to be more detailed) that stores digital data which can be read by a device and interpreted as all sorts of things. This commonly means programs (games, antivirus suites, graphic design utilities, music or video, etc), but nearly any sort of file can be written to a CD—text documents, pictures, proprietary work project files, business card information, and so forth. In some ways, it is like a tiny portable hard drive, unlike MP3 which is a way of organizing information in a self-contained way on something like a hard drive.

Audio CD is a CD (physical medium) which is designed for audio, or is pressed or burned with audio data. Formally released audio CDs will generally meet particular industry standards, ones which surpass your run-of-the-mill blank CDs. Those blank CDs can also be burned with audio data and play similarly to CDs which were pressed by a factory, but most burning processes will not follow the same exacting standards of professionally created audio CDs. The term “audio CD” is often useful in situations where multiple kinds of discs or disc content are included in a product or it is not clear what form certain content will be taking.

So, digital files and physical formats are different because they are different kinds of technologies serving different purposes. They are related insofar as they can work together for us to meet particular goals, like playing some music while driving, but they are independent tools and different types of objects. 

Audio CDs are a particular kind or use of CDs. Sometimes it means that the disc is a special kind of disc which is designed for or mostly limited to burning audio, other times it simply indicates that a disc contains audio (as opposed to video, a program, or other data).

One final thing to mention is that audio CDs should contain lossless audio sources (usually burned as WAV files)—putting MP3s on a CD means you are losing out on quality and versatility. If MP3s are all you have, you can still put them on a CD, whether for archiving or to make a playable disc, but it is better to get the original files or highest quality copies desired when putting audio on a CD. This is particularly true if you are wanting to play something through a speaker system, sell a product, or share audio files with someone who will be using them for something more than just listening (such as composing music or doing forensic analysis).

The compact disc is a miracle of modern technology. Here are some facts:

• They are made principally of injection-moulded polycarbonate.
• The diameter is 120mm.
• They are 1.2mm thick.
• They contain up to 680 megabytes of data. This is the equivalent of 250,000 double-sided leaves (500,000 pages) of A4 text (which would be 83 feet high and need 8 trees to make).
• The music on a CD is imprinted in the form of pits of varying length on a spiral track 3.52 miles (5.66 kilometres) long.
• There are approximately 16,000,000,000 pits 0.11 micro-metres deep.
• The largest pit dimension is 3.054 microns; the smallest is 0.833 microns.
• The width of the pits is half a micron -- which is the distance a human hair grows in two minutes and a fingernail in seven minutes. It is 700 times smaller than a pinprick.
• The space between tracks is 1.6 micro-metres.

Read by a red-light laser beam, the CD plays from the centre to the edge, rotating at a speed varying from 400 times a minute at the beginning to 250 times a minute at the end. This is equivalent to flying round the earth one inch above the surface, up to 400 times a minute, counting every blade of grass on the way.

Your CD is read by the laser beam and makes over 44,000 arithmetical calculations every second in at least two dimensions. It is adding up columns of numbers ('digits'). But many of the numbers are missing because there are thousands of errors on the average CD. Therefore the numbers are added up laterally as well as vertically, enabling the CD-player to fill in the missing numbers by cross-checking them. This is all quite normal and is called 'error correction'.