Both "hold" and "keep" can imply the act of retaining something, but there are some subtle differences between the two words.
"hold" generally implies physical possession or control over something. For example, you might hold a book in your hands, or hold onto a railing for support. "Hold" can also refer to the act of keeping something in a specific position or place, such as holding a door open or holding a ladder steady.
"keep," on the other hand, is more often used to describe the act of maintaining something in a certain state or condition. For instance, you might keep your room clean or keep your car well-maintained. "keep" can also imply the act of continuing to have something, such as keeping a secret or keeping a promise.
In short, "hold" tends to refer more to physical possession or control, while "keep" is more about maintaining something in a specific state or condition.