Focusing is an action where you are more or less in the mind. Focusing on the breath will bring into your experience your deepest aspect, the awareness.
Watching is an action where you are experiencing the awareness and staying as the awareness, where the object of focus in question happens within the awareness.
I recently created a meditation series, in which it starts with Breath Counting Meditation, where we count to ten, one count after each breath, while focusing on the breath. (then the count restarts, and also if focus is lost while counting, we return to the beginning) This will build your concentration, investing more of your energy towards within. The more you practice, the more you will become aware of the awareness.
Next, I included a meditation called the Ujjayi “Victory” Breath meditation. This is a meditation where we focus on the flow of the breath and use the sensations/sounds while the breath passes through the throat area to support us in our focusing. This meditation is a powerful meditation which will effectively bring your mind to a more peaceful state. Here is a which teaches about and guides this meditation. When you practice this, you will start with focus and you will end in greater awareness of the state of awareness.
Afterwards, I included the breath awareness meditation. This is a meditation where we stay aware and focus on the breath. This is a meditation where the standard definition of meditation is practiced (a state of focused awareness). explains this definition of meditation accurately and concisely.
These three steps were meant to give a pathway of practice starting from basic focusing and using the mind to aid in the process, which then progressed by virtue of practice towards just staying as awareness and keeping the attention on the object of meditation. Basically, it is the same thing, it is just that the mind is less active in the last step, so you are aware that you are creating whatever is experienced more as the awareness. The reason for this is you will have already meditated for a while so that the mind has come to more peace.