To be exempt means to not be counted. Thus money or earnings that are not subject to tax deductions is called tax exempted. Legally only a few types of revenue and savings are tax free.
The government as part of its welfare for the needy, does not charge taxes for people with specific income range

Example:
Insurance policies are a unique type of savings where the money allocated over time is not taxed by the government or saving money in PPF or NPS is not counted in your taxable income