What is the difference between these three concepts? I think understand that der Wortschatz can refer to one's personal vocabulary (the set of words that one knows). What of das Vokabel / das Vokabular?
die Vokabel = a single word of your vocabulary (das Vokabular), in particular a single word or phrase you learn when you study a foreign language. Hence Vokabelheft (vocabular book) where you write down these words or phrases.
Vokabular and Wortschatz are mostly synonyms, where Vokabular is either a more formal style level or used for the vocabulary of the certain specific field, e.g. Fachvokabular = (special) terminology, technical terms.
Another meaning of Wortschatz is thesaurus (book), e.g. Der große Lernwortschatz Englisch.
The first meaning of Wortschatz (m.) is: the entirety of the words of a language, as in der Wortschatz des Deutschen; der französische Wortschatz
The second meaning of Wortschatz (m.) is: the entirety of the words someone has at command as in: aktiver Wortschatz; passiver Wortschatz
In both cases, Wortschatz cannot be replaced by Vokabular.
Vokabular (n.) is the entirety of the words someone makes use of as in: Er ist 25 und hat das Vokabular eines achtjährigen Kind[e]s. Here, Wortschatz can be used as a synonym: Er ist 25 und hat den Wortschatz eines achtjährigen Kind[e]s.
Vokabular (n.) can also mean 'the characteristic language of s.o.', as in: a) technisches / juristisches Vokabular or in: b) 'das Vokabular der Politiker:innen / der Pubertierenden, .... a) neutrally denotes what is typical for the language of technicians / jurists, whereas b) often has a more or less pejorative connotation.
Vokabel (f.) is the word as such you are supposed to learn when you learn another language, as in: Vokabeln lernen fällt mir schwer, aber es muss wohl sein.
Note that Wortschatz and Vokabular are usually not used in the plural, whereas (die) Vokabeln probably occurs many times more often than (die) Vokabel (sing.)