I understand the Camelot Wheel is used by DJs to mix songs of different keys together by using adjacent and relative major/minor keys. Can't this same information be deduced from the Circle of Fifths? I don't understand the need for a separate tool for this.
They represent the same exact system it's just presented in a different way. The only differences are it uses colors instead of a key signature to show relationship between keys, spun to have E major/C# minor on top, and labeled with letters and numbers which is presumably to abstract from the concept of a circle related by movements of 4ths and 5ths and think of it more like a clock. A DJ doesn't need to know how many sharps or flats a key has, just know the relationship to other key which seems to be the reason for the changes you see.
If those difference help you then it might be easier to think about it that way, but for musicians the circle of 5ths is presented in a much more intuitive fashion to what we do.
This isn't the only musical system to be reinvented in the modern age. The Nashvile Numbers system is the same as Roman Numeral analysis exact thing except is uses Arabic numerals instead of Roman numerals
The Camelot system is designed to simplify the circle of fifths so that a DJ with no music theory knowledge can easily recognize how similar the keys of two tracks are. From the mixed in key website:
Each musical key is represented by a number and letter combination. The outer ring has Major Chords [sic], while the inner ring shows Minor Chords [sic]. Our Camelot Easymix system makes navigating through keys as easy as counting up and down.
[I believe it should say major and minor KEYS, not chords.]
The wheel essentially renames all the keys. E major becomes 12B, Db minor becomes 12A, etc.
So, a "musician by day and DJ by night" might pick a C major song to follow a G major song because the keys differ by only one sharp. A DJ using the Camelot system would have these tracks labeled in the music library as 9B and 8B, and 8 is close to 9, so we know the keys are similar, without actually knowing what keys they are in or how many sharps they have. The only thing the DJ really needs to learn is how to count "1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 ..."
The circle of 5ths chart you posted is difficult to understand and involves musical terms and symbols. (That I don't know or want to learn about.)
For example: The alphabet goes A,B,C,D... but the the chart goes C, D, G, A....
The other chart you posted is simple and easy to understand and needs no musical knowledge.
For example normal numbers go 1,2,3,4 and the chart goes 1,2,3,4
You only have to look at the chart for 30 seconds to understand what to do with it. You only need to follow common number order and don't have to pay attention to what letter comes after the number because 1a and 1b are in the same box. (You never have to look at the chart again, if you can count.....)
You simply move from 1 to 2 or 1 to 12 just like you would moving around on a clock. Super simple!
This page taught me, it's called harmonic mixing and it lets you make a really easy playlist that sounds great! All you need is a program to tell you want number the songs are. http://www.harmonic-mixing.com/HowTo.aspx
There is a free program called VirtualDJ that will scan your songs and tell you the number. https://www.virtualdj.com/download/
You start with a song that has a number. For the next song, you either pick a song with the same number, or you pick a song with a number before or after your starting number.
You are probably not making a playlist with no musical knowledge involved, but I am. That is the difference in usage between the 2 charts!!
The number of sharps and flats and their placement helps composers to operate with more scales than just minor and major, for example dorian, lydian etc, also composers can easier navigate through other intervals, consonance and dissonance. But I think that's too much for a dj... for most of them eq its enough xD