The various linguistic frameworks all talk about this in different ways, but I think the essence of the question comes down to the observation that in all languages there's a difference between what are commonly called "function words" and "content words" (though they may be affixes, clitics, etc instead of full words.) In any language there will be a set of things you say which have regular, non-figurative, and largely unambiguous meanings, and there will be another larger set of things you say with widespread polysemy and which are more freely used in creative extensions of meaning, and which are easily and frequently coined or borrowed from other languaged. Furthermore, the content words are often analysable as being based off of function words. For example, all verbs can be defined as subkinds of the archetypal verbs BE, DO, and HAPPEN, and all nouns are subkinds of THING. Many linguistic frameworks would analyse every lexical item as either a functional/grammatical lexeme standing by itself, or a functional/grammatical bit of meaning merged with some unique content to form a root.
All languages have grammatical/function words, and new grammatical words can develop over time from content words, a process called grammaticalisation. Wikipedia gives a good summary of four processes of grammaticalisation: semantic bleaching, phonetic erosion, morphological reduction and obligatorification.
As linguistic typology compares languages we have come to identify there are many things which humans talk about in every language. In every language you can talk about how many things there are. In every language you can talk about time. So we can talk about the semantic categories of number and temporality. Furthermore, typology has identified that many of these semantic categories are grammaticalised in lots of languages. While in theory any kind of meaning could become grammaticalised, in practice certain things are grammaticalised far more often. For example, probably every language has grammaticalised at least one of tense, aspect, mood, or evidentiality, and often more than one. So, of the 222 languages in WALS, 45% of them have grammaticalised the perfective/imperfective aspect, and 55% have not, in a very diverse distribution across the world's languages. Languages can grammaticalise very unusual things. In the Australian language Jingulu, every verb marks whether it has an associated motion of going, coming, or remaining in place. We could design conlangs which grammaticalised things which occur in no natural languages, such as whether or not an action is done with a sense of existential millenial dread or irrational baby-boomer optimism.
But despite the possibility of very rare grammaticalised concepts, there are lots of ones which typology has shown are very common. These are what the grammatical categories are, the fruit of typology. Grammatical categories are what working linguists need to know in order to study, make sense of, and document previously undocumented languages. The table below comes from Wikipedia. Linguists familiar with all these grammatical categories will likely be able to account for 90% of grammatical morphemes in any arbitrary language from anywhere in the world. Though language description is never routine, and they're sure to find something unique enough to write a PhD about.