Relation between heat & resistance
Because of Ohm's law, they are equivalent.
Ohm's law tells us that, for an ideal resistor,
$$V = IR.$$
And, in general for any circuit branch, the power consumed is \$P=IV\$.
Therefore, for an ideal resistor
$$P=IV = I(IR) = I^2R$$
or
$$P=IV = (\frac{V}{R})V = \frac{V^2}{R}.$$
And the heat generated by the resistor in some amount of time \$t\$ is just \$Q=Pt\$.
You can use whichever expression for power (or heat) is most convenient, which typically depends on the kind of source that is providing power to the resistor.