A paper cup needs to be waterproof that will handle what's poured into it. The first paper cups were made waterproof using a thin coating of clay, but as you can imagine, this made the drink taste pretty nasty. Wax was also used for a while, then somebody invented PE. PE was a magic solution because it made the cups strong and waterproof, and it had no impact on the taste.
PE stands for polyethylene. It's the type of plastic most commonly used around the world for plastic bags, packaging, and containers. It's also used as a coating on paper cups to make them strong and waterproof. The thing with PE is that it's petroleum-based, which can affect how long it takes for the cup to break down. PE-lined cups can still be recycled, but they have to go through a recycling process separate to other recyclables.
PLA, on the other hand, is made from plant-based materials such as corn starch or sugar cane. It's known as a bioplastic because these materials are renewable resources and it's biodegradable which can be composted totally. PLA breaks down naturally when it's exposed to the environment, and it doesn't leave any toxic residues.