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Rational numbers are integers and fractions
No, not all rational numbers are integers. All integers are whole numbers, but a non-whole number can be rational if the numbers after the decimal point either 1. end or 2. repeat. So, sometimes rational numbers are integers, sometimes they're not. But all integers are rational numbers.
All integers are rational numbers. As a result, there are no such numbers. There is, therefore, no name for these non-existent numbers.
Rational numbers are numbers that can be expressed as the quotient of two integers (3/2, 15/16). All integers, then, are rational numbers (12 = 12/1).
Rational numbers and Real Numbers. The multiplicative inverses of integers are not integers.