What is the difference between the two sentences below? Are they the same or different in meaning?
Jack and Laura's new house is almost ready.
Jack's and Laura's new house is almost ready.
To my perception, the first says two of them have one house and the second says each one has a (different) house (which is almost ready). Is my perception correct?
EDIT: If I don't use "houses" instead of "house" (for my second interpretation), does it mean the sentence is wrong?