Yes, which is why I said that perhaps just the concepts involved might be helpful. I personally found that the explanations one could find in English were not that intuitive, and the technical terms probably don’t help unless you’ve already studied some formal grammar for another language, though some fairly detailed explanations exist, like this one on Wikipedia:
https://en.wiktionary.org/wiki/Appendix:Japanese_verbs#Inflected_forms
However, I can provide something of a starting point with the technical terms here:
You’ve got
未然形=irrealis
連用形=continuative
終止形=conclusive/terminal
連体形=adnominal
仮定形=hypothetical (modern Japanese) / 已然形=realis (classical Japanese)
命令形=imperative
Dictionaries always list them in this order. How can you remember that order? One way is to take AIUEO as the ‘alphabetical order in Japanese’ and to check the final vowel for each form/stem for godan verbs:
未然形 – A
連用形 – I
終止形 – U
連体形 – U
仮定形 / 已然形 – E
命令形 – E
So you get AIUUEE.
The 未然形 is used for negation, and that makes sense because it expresses things that haven’t happened yet (hence ‘irrealis’=not real/realised). It’s also what you attach helper verbs to for the causative and the passive. The 連用形 very literally links to 用言 (‘declinable words’ aka words whose form changes) like adjectives, verbs and adverbs, and can be used to replace the て-form. (In fact, the て-form is actually just 連用形+て historically.) The 終止形 is the one used to end sentences, and the 連体形 comes before nouns to modify them. In modern Japanese, these two are usually identical, so it seems weird that there are two terms, but in Classical Japanese, the two were consistently different. The 仮定形 is the thing we put before ば in modern Japanese, and looks like part of the potential form for godan verbs. In Classical Japanese, if the condition in a conditional statement was not fulfilled and was purely hypothetical, you would use 未然形+ば instead, and if you meant ‘because’ or ‘when’ or something else regarding a condition that was already fulfilled, you would use 已然形+ば, because it’s something already realised (realis). However, as we can see, now, the two usages have more or less merged into the modern 仮定形+ば. Finally, the 命令形 is the one used for given orders, like「いけ！」, and it’s still around today. Another usage of it is in phrases like いずれにせよ, which is roughly ‘whichever one chooses’ i.e. ‘anyway, no matter what, etc.’ In this case, it’s sometimes called the 放任形.
I hope that’s a decent summary. I don’t think I know much more than that, aside from a few random conjugations of old helper verbs and the fact that stuff like the 意志形 (the ‘volitional’, which usually ends in -ou) is the result of a sound change involving む, then う and the あ of the 未然形, which is something I hope to cover at some point in my series (or perhaps just as a random tidbit on Twitter).
PS: The same forms look kind of different for adjectives, and the things they attach to are a little different as well, but I don’t think I’ll go into those right away, and you’ll probably come across them after you’ve taken a look at verbs.
