Consider:
“Er steht früh auf.”
That’s four words. “Steht” is a word and so is “auf.”
With the example sentence, the conjugated use of the verb is three morphemes.
- steh-: The root morpheme, meaning to “stand.”
- -t: The inflectional suffix, for third person singular in the present tense.
- auf-: The separable prefix, modifying the meaning with “up.”
The lemma is “aufstehen.” What you’ll find in the dictionary. Base word can be considered as a synonym as it’s uninflected and serves as the foundation for generating other forms.
The abstract unit of meaning that represents the base form of a word and all its inflected variants, here for “getting up,” is the lexeme.
The lexeme “aufstehen” has a number of word forms across tenses, moods, and persons, such as the following few examples:
- ich stehe auf (I get up)
- du stehst auf (you get up, singular informal)
- er/sie/es steht auf (he/she/it gets up)
In casual speech, “word” could many any or all of these without much concern for linguistic precision, but if we’re talking about relationships or ratios, there may be benefit of precision of what we’re talking about.
In German linguistics, research on the ratio between lexemes and word forms indicates a complex relationship due to the rich inflectional nature of the language. Studies suggest that a single lexeme in German can correspond to multiple word forms, often ranging from 3:1 to 10:1.
Perhaps look at this where German is mentioned and the referenced studies for more info.
Related, LingQ used to have a published table on what threshold number of what-LingQ-counts-as-words it takes to advance by different levels. I don’t know the current status on that, but saw this fairly recent thread.