The OP's description seems confusing. I'll try providing a better summary.

Full-Node

A full-node is the term for "fully validating", which means this type node checks both transactions and blocks itself, without trusting others to do that. Note that miners will usually be full-nodes, because if they don't they risk losing money as they might waste hash power on an invalid block.

Light Node or SPV (Simplified Payment Verification) Node

A "light" or "SPV" node does not verify all transactions or blocks independently. Instead, this type node relies on other nodes to check whether or not transactions it is concerned with are in the valid blockchain. In many situations this reduced independence is fine for making simple transactions, and this type node uses far less resources since it doesn't deal with entire blocks.

An example of a popular Bitcoin SPV wallet is Electrum: https://electrum.org/

The advantage of using both types is completely controlling your own private keys, which is recommended (as opposed to leaving coins on exchanges).