The important feature is that in a polysynthetic language, a single word may contain more than one lexical root.
This means that e.g., to choose the most frequent example, a complex verb may not only contain the verbal root, but also an incorporated noun, which (as opposed to compounding) remains referentially autonomous (In compounds, transparency often gets lost, like straw in strawberry, while incorporated items keep their referential meaning more clearly.) and satisfies the verb's argument positions (When the verb requires an object, it will be satisfied by the noun that was incorporated so there are not any more words in the sentence that the verb would take to fill out one of its argument positions.).
The incorporated items are contained in the word complex in such a way that they may be surrounded by further morphemes (like prefixes, tense affixes or person inflection in verbs) which are an inherent part of the verb as well, so you can no longer regard the incorporated parts as separate words. They are actually an inherent part of the verb complex itself and cannot simply be detached without changing the word's meaning.
Velupillai (2012:109) illustrates the difference by the following example:
"The crucial difference between synthetic and polysynthetic words is
that the latter involve more than one lexeme. While the Turkish
example in (49) is very long and involves a great deal of segments,
there is only one lexeme, tan ‘know’. Polysynthetic words, however,
may contain more than one lexeme: [...] The Alutor word contains three
different lexemes, akka ‘son’, nalgə ‘skin’ and kuww ‘dry’."
Therefore, while both words are equally long, "the Turkish word is
synthetic while the Alutor word is polysynthetic."
As for the question of what a word is, this is a bit more difficult.
First of all, a word is a lexical unit that can stand on its own, so car is a word, engine is a word, blue and scream are too, but un- or -ation are not.
This mostly boils down to the distinction between free and bound morphemes, with some borderline cases like confixes (fanat-) or so-called cranberry morphemes (cran-berry).
Now since both car and engine can stand alone, the question is whether they are actually one or two words.
This is not always as easy, but there are certain properties of words which help to determine a word complexes status (partially relying on Velupillai (2012:117):
- phonology: a word is pronounced as one phonological unit; this having
consequences on, e.g., stress, as mentioned by @Atamari: There is
a difference between mEtalworker (a person who works with metal)
and metal wOrker (a worker made of metal, e.g. a robot) --> when
stress is changed, a new word was formed; and you would assume the
former to be one word and the latter two, because one could regard
metalworker as an independent lexeme with a rather fixed meaning and possibly an own lexicon entry, while metal in metal worker is
rather a modification that describes further properties of worker, but is not an inherent part of its meaning.
- inflection: Compound words are typically inflected as one (by their head), rather then the invidual morphemes being inflected individually: footballs (not * feetballs), car engines (not * cars engines)
- coherence: Words that behave as one unit can not get broken up by other words that, for example, modify them: new football (not * footnewball), broken car engine (not * car broken engine)
- semantics: This makes use of the assumption that a word is the smallest unit in a sentence in which meaning is preserved; you could for example ask yourself whether a single (= "alone bringing-up" mother is still a single mother when she moves in with another single mother, i.e. whether single mother is one conventionalised word (usually meaning that the father is missing, not necessarily that the mother lives all alone) that preserves its meaning throughout different contexts, or whether single is barely a compositionally derived modification of mother that doesn't make sense to use compositionally in a different context.
There is also a difference between a morpho-syntactic word and a phonological word, e.g. the single phonological word don't (no pause in between, and in this case also morphological mering) consists of two morpho-syntactic words do and n't, which have certain morphological properties and are correspondingly represented in syntactic analysis.
I personally would actually argue that English car engine is just as much a compound as German Automotor is and thus to be seen as one word, due to the stress behaviour and due to its lexical status (One might assume that car engine has to some exted a conventionalised meaning and possibly even an own lexicon entry. Intuitively I'd say there is some difference in straightforward interpretability or meaning predictability when changing the word to racing car motor.), where idiosyncratic spelling rules should not influence linguistic categorisation too much.
See also this question for an attempt to describe when English compounds are separated by a space and when not (note that this question already presupposes that English compounds are indeed to be regarded as a word, the terminology would not make much sense otherwise, since compounding is by definition a word formation process).
Velupillai, Viveka. 2012. An introduction to linguistic typology. John Benjamins Publishing.