Savings for what? If you want to get into specifics for this kind of thing... you need to look into the tax code for the government you're interested in.
In the united states, income includes wages, interest on savings, dividends on investments, self-employed income, gains from bartering and stock sales, rental income, etc.
However, there are specific ways you can *save* income so it gets excluded from income, such as an MSA/HSA/ESA, etc. This question can really be vastly different depending on which country you are asking it about.