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.
Mein Wagen ist neu, aber deiner ist neuer.
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
Ein neuerer Wagen wäre ökologischer.
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.