How a letter rotation works
A Caesar cipher replaces each letter with the one a fixed number of places further along the alphabet, wrapping from z back to a. With a shift of 3, attack at dawn becomes dwwdfn dw gdzq. The shift is the only secret, and because the alphabet has 26 letters there are just 25 useful shifts. A shift of 26 returns the original text.
ROT13 is the Caesar cipher with a shift of 13, which is special because 13 is exactly half of 26. Shifting by 13 twice moves a letter 26 places, back to where it started, so one operation both encodes and decodes. That symmetry is why ROT13 became the convention on Usenet and in early forums for hiding punchlines, puzzle answers and spoilers: no separate decoder is needed. Pairs such as abjurer and nowhere are ROT13 of each other.
What each mode changes and what it leaves alone
ROT13 and Caesar modes rewrite only the letters A to Z and a to z, keeping each letter's case. Digits, spaces, punctuation, line breaks and non-ASCII letters pass through unchanged, so an accented é or a Cyrillic word survives but is also not disguised. The Caesar shift field accepts 1 to 25. A value outside that range is clamped when you leave the field, and non-numeric input becomes 1.
ROT47 works on the ASCII printable range instead. It takes every character from ! (code 33) to ~ (code 126), 94 characters in all, and moves it 47 places along that range, wrapping at the end. Letters, digits and symbols all change. The space character and anything outside ASCII do not. Because 47 is half of 94, ROT47 is its own inverse in the same way ROT13 is, which is why the mode has no Decode toggle.
Decoding text you were given
If you know the text is ROT13, paste it in with ROT13 selected and the output is the plaintext. If you only know it is a Caesar shift, switch to Caesar / ROT-N, tick Decode, and step the shift from 1 upwards. One of the 25 settings turns into readable words. Short texts can be ambiguous, but anything longer than a sentence has only one shift that produces real language.
Text that still looks wrong after all 25 shifts was probably not a plain Caesar cipher. Check whether the digits and punctuation changed too (then try ROT47), whether the letters are grouped in fives or lack spaces (a sign of a different classical cipher), or whether the string ends in = signs and mixes upper case, lower case and digits, which points to Base64 rather than a rotation. The Base64 decoder handles that.
Why none of this is encryption
A rotation has no key worth the name. The Caesar family has 25 settings, ROT13 and ROT47 have one each, and letter frequencies survive the transformation: the most common symbol in the ciphertext maps to e in English text of any length. Anyone who recognises the pattern reads it as easily as you do, and so does every piece of software written to look for it.
That is fine for the jobs ROT13 is used for: keeping a spoiler out of the corner of someone's eye, obscuring a puzzle answer below the puzzle, or making a string survive a filter that matches on plain words. For passwords, secrets or anything a stranger must not read, use real encryption or a hash. The MD5 generator shows what a one-way hash looks like by comparison, and the difference is the point: ROT13 goes both ways by design.