Starter noise Toyota 1993 Camery?

Good battery but when ignition is engaged by key, sometimes it makes a noise like Sheunk and then no more sound as we continue to turn the ignition on. Lights and everything work fine but the starter won’t engage the engine.

Is this a starter problem?

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It souds like the starter solenoid is failing. Some engines, esp, the newer ones have the solenoid built into the starter, others it can be replaced seperatly.
sometimes if the battery terminals are corroded or if the battery is very low on charge, you will get this same problem, so you need to check that first. The head lights might come on even if the battery is not able to send enough current to the starter to turn over the engine, because they dont draw as much current. nothing on you car will draw the way the starter does, and that is why it has a solenoid sw. and the lights only have a relay.

Likely the starter solenoid contacts, they wear out on Toyota starters. Google ‘Toyota solenoid contacts’ for more information.