I saw a spelling mistake on an SO question: submittion. That got me wondering, is there a name for the shift of ‑mit‑ to ‑miss‑ in submission, permission, admission and so on? Are there other patterns like this in English words? (Not simple stuff like dropping an e for confuse/confusion) and if so, are these patterns related to the language we took the word from?
Compare the latin admittere and admittionem. In the latter form the coronal stop [t] is followed by a high front vowel. A stop--high vowel sequence is one of the most common sources for a consonant mutation (generally, a sound change where a consonant's sound value is altered due to effects of a neighboring vowel). Well-known examples of consonant mutation are found in Celtic and in Bantu languages.
When a stop is changed to a fricative, the change is usually referred to as lenition (weakening). More specifically, when a stop changes to an affricate or fricative, it is called spirantization. Most specifically, when a stop or fricative preceding a high front vowel/semivowel undergoes change, it is called palatalization.
Some other alternations involving Latinate words which presently show a palatalization alternation:
Note that in some cases the alternation is reflected in the spelling (as in submit/submission), but in others the same consonant letter is used with different sound values (as in confuse/confusion). As a commenter points out, submissio was already spelled with an s in Latin.
Shifts of this sort are very common in words of Latin derivation. In the case you cite, missus is the participle of mittere, and the nominal forms of admit, commit, emit, permit, remit all take the terminal -ssion form. (Promise represents the same thing, though in this case the verb is a back-formation from the participle used as a noun, promissum, and there is no promit, at least today.)
Latin underwent many sound changes which caused stems to have different terminal vowels in different conjugational and declensional contexts. Here's just a handful of examples from what must be hundreds of words represented in English:
In other cases, such as those pointed out by jlovegren, the change took place after the word was borrowed into another language and involved only one of these consonants — but that one took on two different pronunciations, depending on the phonological environment: regal/regicide, for instance. Sometimes English has borrowed a stem twice, once from Latin and once from its French daughter: alongside regal and regicide we have royal — and in that particular case we also have a descendant from an entirely different line of descent, rajah.
And similar pairings occur in “native” (Germanic) English words: was/were is the most common example, but consider also life/live, think/thought, lose/forlorn.