Some kanji dictionaries will list every word that starts with that kanji (within reason). But then the words that end with that kanji are of course scattered all over the book in other kanjis’ entries. And definitions tend to be no more than a short sentence. As Naph said, the focus is on the kanji itself, not the words as much.
As you can see, the kanji one will have a lot of kanji-related explanations the kokugo one doesn’t have, such as radicals, stroke order and origin. Since it is a kids oriented one it also has a box explaining the difference from another kanji that has the same reading and a close meaning (街), what is very³ useful. It does try listing the most common vocabularies with that kanji, but of course it is 1. impossible covering everything and 2. each entry is a raw line that doesn’t help you that much.
The kokugo one, on the other hand, is the same thing you call a dictionary in other languages. Each entry is a word (note that it treats 街 and 町 as the same word since the meaning is so close, and unfortunately doesn’t go over the difference), but one word can have several meanings. Since it is meant for kids, they usually have plenty of example sentences, what is very³ useful, specially with verbs. Even if you know the meaning of a verb, you might feel lost about what particle to use and checking the sentences helps a lot.
As @Leebo said, searching a specific word in a Kanji dictionary can be a hell, because you literally don’t know where it is. It’s meant to be used for searching kanji, not words. About you question, I think both are written pretty much the same way, using kanji but with readings for everything.
As your first dictionary, I would recommend a kokugo one, too.
End up getting the 例解 Kanji one since it turns out they have a nice app of the 例解 国語 one.
Is there a list somewhere of some common japanese dictionary verbiage that I could prestudy to help ease comprehension? Im assuming since they are aimed at kids, the style of defitions would be similar throughout the book.
As of now, I just plan on using it to look up as many things as possible and see where it gets me
It won’t take you long to get used to the format of dictionary entries and common words.
物事 (ものごと) - things (general word for not specifying a particular noun), usually abstract or non-physical things
事柄 (ことがら) - matter, circumstances
〜こと - used to make a noun phrase
〜さま - the state of (used in adjective definitions)