Jisho

I think the former is more about the vocabulary or words you e.g. put into flashcards to learn, while the latter is about one's vocabulary in the sense of "the way one expresses themselves". That's just based on my feeling though

When comparing the definitions from e.g. the 三省堂国語辞典 for these two the distinction can also be noted:
単語:

文を組み立てている最小の単位で、決まった意味や文法的役割を持つことば。語。例、「今夜、雨が降るらしいよ」の「今夜」 「雨」 「が」 「降る」 「らしい」 「よ」。

"The smallest units forming a sentence, words carrying a fixed meaning or grammatical role"

語彙:

①ことばの集まり。
「━と文法」
②ことばを類別して集めたもの。

"Collection of words, i.e. (a/one's) lexicon, vocabulary"

Second sense also mentions the classification often done inside a 語彙.

Hope this helped