At the Tuesday desk, the first card on the table is an account. People arrive with a picture of a login and a balance. The picture is only half useful. On Solana, an account is a record at an address. The address is a public key. The record is what the cluster stores for that key.
Four fields matter before any program is interesting. Lamports are the unit of value sitting in the account; one SOL is one billion lamports. Data is the byte array the account stores, which may be empty. Owner is the program allowed to change that data. Executable marks whether those bytes are a program the runtime may call.
Owner is the field people skip
Beginners stare at the balance and miss the owner. A wallet account is usually owned by the system program. That owner is what lets a signed transfer change the lamports. A data account used by a custom program is owned by that program. If you ask the system program to write those bytes, it will refuse, because it is not the owner.
In the reading room we draw two boxes. The left box is the account. The right box is the program id named as owner. The pencil line between them is the whole of week one. If you can say that sentence without looking down, you are ready for signatures.
A wallet is one kind of account
The word wallet describes software that holds a secret key and builds transactions. The account is the on-cluster record. You can have an account with data and no friendly wallet screen. You can have a keypair in a file and no account yet, until a transaction creates one and funds the rent-exempt minimum.
When a nephew or a colleague says 'my account', ask which they mean: the keypair in an app, or the record with lamports, data, and an owner. The Beginner Concept Desk spends the first evening on that question and does not move on until the group can answer it with the card face up.
See the Beginner Concept Desk if you want these chapters read with a group.