Step 1: Fix what happens at the cathode in both cases.
In both setups, whether the electrodes are silver or platinum, the cathode reaction stays the same. $Ag^+$ ions from the solution are simply reduced and deposited as silver metal, because silver is easier to reduce than water here.
Step 2: Ask whether the electrode itself can react.
Platinum is chemically inert, it just hands over electrons and does not take part in the chemistry itself. So at a platinum anode, the only thing available to be oxidised is water, which is oxidised to oxygen gas, releasing $H^+$ ions.
Step 3: See what changes with a silver anode.
A silver anode, by contrast, is an active electrode, oxidising silver metal itself to $Ag^+$ actually requires less energy than oxidising water. So instead of any gas being released, the silver anode itself dissolves away into the solution as $Ag^+$ ions.
Step 4: Compare the outcomes.
With platinum electrodes we see oxygen gas bubbling at the anode, with silver electrodes the anode simply erodes and no gas appears at all, even though the cathode behaves identically in both cases.
\[ \boxed{\text{Pt anode oxidises water to } O_2\text{; Ag anode oxidises itself, since it is an active electrode}} \]