The 4th house in your chart reveals your base. For example, if Saturn rules your 4th or if Saturn in placed in your 4th house, I would consider you to be fear-based. If Jupiter ruled your 4th or was placed there, I would think of you as faith-based, etc.
The 10th house is public, the 4th house is not. Whatever is described by your 10th house is there to be seen by the public. In contrast only you and your intimates are likely to be aware of the qualities described by your 4th house. You do have to consider the entire chart as there are exceptions to this and I can serve as an example.
Mars rules my 4th house so at my core, I am driven, angry, ambitious, heroic, etc. Mars in my chart is in the 9th house, conjunct Mercury so I broadcast these qualities. I flat our state that if you break into my house (4th), I will shoot you (Mars).
See how cool astrology is?
How does your 4th house describe you?