お待たせいたしました。(Just a little example of keigo as a joke ) It’s rather long. I’ll take your classification and complete it + add some corrections.
I’m not sure if I can give you a ‘morphological’ classification, but in my opinion, and based on the Japanese textbook I have, there are three levels of politeness in spoken Japanese:
①とても丁寧な言い方: very polite speech, which uses 敬語 (honorifics). There are two kinds of 敬語:
ⓐ尊敬語: ‘respectful’ speech (elevates the status of the listener; I don’t know how this is translated in textbooks)
ⓑ謙譲語: humble speech (lowers the status of the speaker)
Side note: it also seems that some 敬語 can lower the status of the listener if used to indicate their actions. (I found that out while reading the definition of 参る.) In that case, it’s 尊大語, which elevates the speaker above the listener. I imagine such usage is rare now, since probably only people of very high status would be able to say such things. (I don’t know if it would be acceptable even for the Emperor to use this.)
②丁寧な言い方: polite speech, which can be combined with 敬語 where necessary. Typically characterised by the です・ます forms.
③くだけた言い方 ≈ タメ口 (The categories that follow are just descriptions. They’re by no means technical terms.)
ⓐ Casual speech
ⓑ Vulgar speech/slang
タメ口 is strictly speaking a term used by young people to designate speech without honorifics and polite forms, which literally means ‘equal mouth’. I guess you could call it ‘plain speech’? The term itself isn’t a technical term though, since it’s rather informal.
辞書 形 (形 means ‘form’; 系 is often used to mean ‘system’ or ‘series of interconnected things’, which isn’t quite what we’re discussing here) forms the basis of the 砕けた言い方, but as my friend studying in Japan often told me, this so-called ‘dictionary form’ isn’t necessarily casual, since it can be used in formal writing, like scientific journal articles, and as YanagiPablo pointed out, even the verbs used in 敬語 can be used in their 辞書形 when necessary.
In terms of morphology… you could say that each speech level has its own morphology, but it’s not like they’re unrelated. Dictionary form is just the ‘plain’ form of the verb without です・ます, while polite speech usually uses the ‘masu stem’, which is called the 連用形 in Japanese. 連用 because 連=connect and 用=用語, which are the words that have declinations/multiple forms in Japanese, like verbs. 敬語 usually either uses a different verb, or takes the 連用形, adds お, and then になります behind it (to describe the listener’s actions, that is). Those are just some general ideas. 敬語 morphology is of course a little more complex, and there are things I don’t know.
What YanagiPablo just said as an explanation is accurate, but I think ‘relationship’ (or rather, ‘closeness’) and ‘respect’ aren’t necessarily two distinct concepts. It’s true that in some anime (and I think also in period dramas, though I’ve only seen one), children in noble families often address their parents using honorifics (e.g. お母様 or 母上 instead of the usual お母さん), but generally speaking, closeness tends to preclude the need for politeness. For example, while we might use it as a joking reference to Japanese grammar practice between Japanese learners, it would be quite shocking if one of us suddenly transitioned into polite or honorific speech when speaking to a close Japanese friend. I’d say it’s more like a tree:
a. Ordinary politeness (丁寧語)
b. Increased politeness (丁寧語+敬語)
Each time you go up a level, you add additional components.
[Edit: merged posts]