[THEORY] Accidentals and enharmonic notes

Hello all you beautiful people and welcome to our 2nd theory topic. The first one I feel was a bit too big, so we’re going to tone it down a bit and talk about accidentals and enharmonic notes.
Accidentals are musical symbols used to alter the pitch of a note. Now there are five of them in total, 3 of which are a tad more common than the others:

the sharp accidental (symbol), which raises the pitch of a note by one semitone
the flat accidental (symbol), which lowers the pitch of a note by one semitone
the natural accidental (symbol), which reverts the pitch of a note to its natural state
the double sharp accidental (symbol), which raises the pitch of a note by two semitones (or 1 tone)
the double flat accidental (symbol), which lowers the pitch of a note by two semitones (or 1 tone)

I would have embedded the symbols directly into the post, but I don’t know if it would have worked. Anyhow, the latter two are used mainly when chromatic scales are involved, or so I’ve heard. I don’t think I’ve seen them used in any of the sheets I’ve ever played. The first 3 however are very common in songs.
The second subject of today’s topic involves enharmonic notes. While the name may sound fancy, the explanation is very simple. Enharmonic notes are notes that have the same pitch but with different names. In other words, we are referring to two notes that sound exactly the same but, due to key signatures and the circle of fifths, have different names. Examples include but are not limited to: C# – D flat, E# – F, C flat – B and so on.
That’s it for today’s topic. If you feel that I am going either too fast or too slow, let me know. A word of advice would be to take your time with these concepts and make sure you fully understand them. If you have any questions, feel free to ask them.
Previous posts in series:
Notes, pitches, semitones and octaves

Aa yes. I knew I forgot something.
On a guitar a semitone is equivalent to a one fret distance on the same string. For example, on the E string, if you play the open string and then the note on the first fret, which is F, that is a semitone or half step.
Same thing for tones or steps, only it’s a two fret distance.

Not necessarily a simplification. Just another way of looking at things based on the key signature, as you’ve mentioned. Papa Gates explains the circle of fifths very well in one of the tutorials.
But at the end of the day the C# and D flat notes are one and the same, pitch wise.