Yes, there is a difference.
Plated bullets start as a lead core that is submerged in a chemical bath and electroplated with copper. The copper that attaches to the lead core is very thin. The thin plating is easily damaged if used at high velocities (typically when supersonic) or if crimped too tightly etc. They are usually cheaper than a standard jacketed bullet, however.
Jacketed bullets have a thicker, copper cup made and the lead core is encased in said cup/jacket. It is quite a bit thicker than plated bullets, and can withstand high velocities and is generally more durable and less susceptible to the jacket coming off or being damaged from tight crimps or in the rifling of the barrel. They are more expensive usually when compared to plated.