Step 1: Frame the statements.
We judge two claims about symmetry and echinoderms.
Step 2: Examine Statement I.
Radial symmetry means any plane through the central axis cuts the body into similar halves, as in starfish and jellyfish. This definition is correct.
Step 3: Look at adult echinoderms.
Adult echinoderms such as starfish and sea urchins show radial symmetry.
Step 4: Look at the larvae.
Echinoderm larvae, however, are bilaterally symmetrical, not radial.
Step 5: Judge Statement II.
Statement II claims both adults and larvae are radial, but the larvae are bilateral, so Statement II is incorrect.
Step 6: Conclude.
Statement I is correct but Statement II is incorrect, which is option 4.
\[ \boxed{\text{Statement I correct, Statement II incorrect}} \]