1. Rot13: "Colorless green ideas" ⇒ "Pbybeyrff terra vqrnf". This method is familiar to old Usenet denizens. It makes use of the fact that the Latin alphabet has 26 letters by rotating them 13 places (a⇒n, b⇒o, ... m⇒z, n⇒a, o⇒b, ...) and so this method is its own inverse. That is, you decode a rot13 message by doing rot13 on it a second time. This is a special case of a Caesar cipher. Such ciphers are not very arbitrary as they mostly preserve alphabetic letter order, but they "wrap" the alphabet around into a circle (like color in the visual system) with "z" being followed by "a". In a rotation cipher, once you figure out one of the letter codes, you've got them all. So if "s" maps to "e" then "t" maps to "f" and so on.
2. Scrambled alphabet cipher: Randomly permute the 26 letters to other letters, for example A..Z ⇒ PAYRQUVKMZBCLOFSITXJNEHDGW. This is a letter-based codebook. This is arbitrary, at least from the individual letter perspective, as it won't preserve alphabetic order, encoding "Colorless" as "Yfcftcqxx". So knowing one letter mapping (c⇒y) won't let you automatically determine the others.
But this cipher does preserve various other properties, such as capitalization, number of distinct atomic symbols, spaces between words, message length, doubled letters, and sequential order in general.
Even word-based code books tend to preserve sequential order. That is, the message is input word-by-word from the beginning of the message to the end. But more sophisticated methods are possible, for example by padding the message with irrelevant words. It's less common to see the letters of the individual words scrambled, but we could do that for words of varying lengths, say by having words of length 2 reversed, 21, so that "to" would be encoded as "to" ⇒ "ot" ⇒ "fj". And words of length three might be scrambled 312, length four as 2431, and so on, choosing a random permutation for each word length. Adding this encryption technique will break apart some doubled letters. But the word order would still be preserved across the encryption.
These toy examples are just to show that "arbitrary" vs "systematic" isn't an all-or-nothing thing in a mapping. You have to consider all sorts of properties of the input and output representations and see which properties are being systematically preserved (or approximately preserved) across the mapping, and which are not. Temporal relations (like sequencing) are particularly important in this respect.