In a blockchain, the term “client” pertains to software that connects other software, (which are labelled clients as well), in a peer-to-peer manner. As these communicate with each other, the clients form a network wherein each of these is a node. This explains why the term “node” is interchangeable with the term, client.
A client is able to access and process blockchain transactions within a local computer. One good example of a client is a cryptocurrency software wallet.
As for the case of Ethereum, there was formerly only one classification of a node, referred to as a “Full Node”. The software is in charge of verifying and relaying transactions and blocks on the network. In light of the trustless environment and the nature of blockchains, each full node has to download and verify the blocks individually, hence every single transaction in each block.