A contract, in the SDK, is an abstraction that represents a connection to a specific smart contract deployed on the Fuel Network. This contract instance can be used as a regular Rust object, with methods attached to it that reflect those in its smart contract equivalent.
A Provider is a struct that provides an abstraction for a connection to a Fuel node. It provides read-only access to the node. You can use this provider as-is or through the wallet.
A Wallet is a struct with direct or indirect access to a private key. You can use a Wallet to sign messages and transactions to authorize the network to charge your account to perform operations. The terms wallet and signer in the SDK are often used interchangeably, but, technically, a Signer is simply a Rust trait to enable the signing of transactions and messages; the Wallet implements the Signer trait.