Parachains are individual blockchains having their own data structures designed to address specific use cases. They work independent of each other and are connected to the relay chain. Each Parachain is like an execution slot on the polkadot framework and various Parachains operate in Parallel to execute transactions effectively separating the transaction submission and finality. Moreover, the Parachains can communicate with each other and exchange any type of data within themselves.
Parathread is another way of participating in the Polkadot consensus mechanism wherein the Parathread submits transactions and participates in the shared consensus in a block to block basis. It does not involve the parathread to stake $dot to reserve a parachain slot.
The parachains and parathreads are connected to the relay chain which is the core of the polkadot framework. The relay chain validates the transactions and acts as a mechanism to achieve transaction finality and acts as a source of truth for the parachains.
Collators collect the transactions that occur in a particular parachain and submit the same to validators for validation of the transactions on the relay chain.