Is it true that neuer can stand for both - and thus the only way to figure out if it's newer or just new is by context?
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Yes, both sources are correct. The regular comparative is formed with the ending -er, so "neuer" is the comparative of "neu":
Then we have the endings in the declension of adjectives, and yes, for the indefinite article, the nominative ending is also -er:
Yes, it sounds confusing, but we all will just have to live with it ;)
Yes, they can mean both. Now how to distinguish between them.
If an adjective stands in front of a noun it will get some sort of ending depending on case, preceding article and numerous. One possible ending is -er. The minimum ending is -e. There will never be no ending. So if you see "neuer" in front of a noun, the -er MUST be an ending and the word is hence just "new" (neuer - ending-er = neu). If neuer is not in front of a noun but rather a complement to a verb, then it means "newer" as it has no ending there.
If you have "newer" in front of a noun, then the basic adjective is "neuer". This will then get the appropriate ending leading to such beautiful words like... neuerer
Side-note: I doubt that every German would notice if you said "neuererer" as long as you say it fast and with confidence. To some it might even feel right after you told them what you did.
"Neuer" has two functions:
Since 1) is not declined, then you will decline it when needed, so eg you will say
etc. (but "mein Wagen ist neuer", however there's no ambiguity since the non-comparative form would be "mein Wagen ist neu").
a new car / a newer car:
the car is new / the car is newer: