PARACHAINS: Application -Specific data structures that is globally coherent and validatable by validators of the relay chain. Parachains are able to parallelize transactions processing and achieve scalability. Parachains have a dedicated slot (core) for their chain and are like a process that runs constantly. Parachains are maintained by the network maintainer known as a collator.Role of the collator is to maintain full node of parachain, retain transaction information of the parachain and produce new block candidates to pass to the relay chain validators for verification and inclusion in the shared state of polkadot.
PARATHREADS: Parathreads are an idea for parachains to temporarily participate (on a block by block basis) in Polkadot security without needing to lease a dedicated parachain slot. This is done through economically sharing the scarce resource of a parachain slot among a number of competing resources (parathreads). Chains that otherwise would not be able to acquire a full parachain slot, or do not find it economically sensible to do so, are enabled to participate in Polkadot’s shared security — albeit with an associated fee per executed block. They have the exact same benefits of connecting to polkadot that a full parachain has. It also offers a graceful off-ramp to parachains that no longer require a dedicated parachain slot, but would like to continue using the Relay Chain.
RELAY CHAIN:The Relay Chain is the central chain of Polkadot. All validators of Polkadot are staked on the Relay Chain in DOT and validate for the Relay Chain. The Relay Chain is composed of a relatively small number of transaction types that include ways to interact with the governance mechanism, parachain auctions, and participating in NPoS. The Relay Chain has deliberately minimal functionality - for instance, smart contracts are not supported. The main responsibility is to coordinate the system as a whole, including parachains. Other specific work is delegated to the parachains, which have different implementations and features.
All blockchains on Polkadot(via Parachains/Parathreads) are connected to the relay chain.
Allows Polkadot to process transactions from all chains in the network at the same time.
Provides a secure way for chains(on Parachains/Parathreads) to communicate with each other.