Step 1: Start from the general rule about $p\pi$-$p\pi$ overlap, before touching carbon specifically.
Two atoms can form a strong $p\pi$-$p\pi$ bond only when their p orbitals are close in size and energy, which happens for small, second-period atoms like C, N, and O. Once atoms get bigger, their p orbitals become larger and more diffuse, and side-on overlap becomes too weak to hold a stable multiple bond.
Step 2: Apply this rule to carbon, which is what Assertion (A) claims.
Carbon is small and sits in the second period, so it satisfies the size and energy-matching condition. It readily forms $p\pi$-$p\pi$ bonds with itself, as in $C=C$ and $C \equiv C$, and with other small electronegative atoms like N and O, as in $C=N$ or $C=O$. Assertion (A) fits the general rule, so it is correct.
Step 3: Apply the same rule to the heavier group 14 elements, which is what Reason (R) claims.
Silicon, germanium, and tin lie in the third period and below, so their p orbitals are much larger and more diffuse than carbon's. Side-on overlap between such large orbitals is too weak to support a genuine $p\pi$-$p\pi$ bond, which is exactly why compounds like $Si=Si$ are unstable or need special stabilisation. Reason (R) goes directly against the general rule, so it is false.
Step 4: Decide the relationship between A and R.
Since R is factually wrong, it cannot explain A, whether or not A itself is true.
Final Answer:
\[ \boxed{\text{(A) is correct but (R) is not}} \]