Either answer is correct, depending on what number system and arithmetic system you are working in.
If you are working with just integers, using standard grade-school integer arithmetic, then it is completely correct to say "12 divided by 48 results in 0 remainder 12."
There are no fractional integers, so numbers like $0.25$ don't exist in that arithmetic system.
If you are working in rational numbers or real numbers, then $12/48 = 1/4 = 0.25$.
Most calculators are designed to work with decimal numbers with fractional parts,
which is a kind of rational number, so their answer to the division will be $0.25$.
You can use an ordinary calculator to help you do integer arithmetic, but you have
to realize what the results mean to you. The integer quotient is only the part to the
left of the decimal point; anything to the right of the decimal point is an indication
of a remainder. But you have to multiply that fraction by your original divisor to get
the true integer remainder. For example, on the calculator,
$$ 72/48 = 1.5.$$
So the integer quotient is $1$. To find the remainder, we take just the "fractional"
part of the calculator's result, namely $0.5$ in this case, and multiply by the
$$ 0.5 \times 48 = 24.$$
Therefore 72 divided by 48 results in 1 remainder 24 in integer arithmetic.