What the income documents actually prove
Two certificates are asked for and they are not interchangeable.
課税証明書 (taxable income certificate) states the income assessed for a year and the tax charged on it. It is what the office reads to judge whether the household can support itself.
納税証明書 (tax payment certificate) states whether that tax was actually paid. Unpaid residence tax is a recurring cause of trouble, so clear any arrears before requesting it — the certificate then shows nothing outstanding.
Both are the Japanese spouse's, obtained from the municipality where they pay residence tax. If the household's income comes from someone else — a parent acting as supporter — the certificates follow that person instead.
Where income was below the taxable threshold, no 納税証明書 (tax payment certificate) exists because there is no tax to certify. The office issues a 非課税証明書 (certificate of non-taxation) instead. Submit it, and show separately how the household is funded: savings, the other spouse's earnings, family support. An unexplained gap is what invites a request for more documents.
A recent job change is worth explaining before it is noticed. The tax certificate reports last year, so someone who changed employers three months ago will have a certificate showing the old salary. An employment certificate and a recent payslip close that gap in one step.