What is common among these three? In all these three (mindfulness, absorption, and contemplation), you bring your attention to an experience or subject, and you sustain your attention on it, by your choice.
Now to the difference.
When you practice mindfulness, you don‘t lose yourself in the experience you are placing your attention on. If you are noticing your breath, you don’t absorb yourself completely in the sensations of the breath. Instead, you stay present as a witness—the sensations of the breath arise and pass in your awareness, but you are separate from the breath.
When you choose absorptive meditation, you want your awareness and your sense of self to become one with the experience. If the breath is the target of your attention, you let your awareness become one with the sensations of breathing. Your goal is to lose awareness of yourself.
In the above two, you are directly experiencing the target of your attention.
When you engage in contemplation, you are thinking about an experience in words or thoughts. Contemplation is an exercise in reflection on, rather than presence with, or absorption in, an experience. If you are contemplating your breath, you are reflecting, using words or thoughts in your mind, on the experience of breathing and anything else related to breathing.
In yogic Sanskrit, mindfulness is smrti-sadhana, absorption is samadhi, and contemplation is svadhyaya.
Readers with deeper exposure to the yogasutra and the study of meditation may realize that mindfulness meditation and absorptive meditations merge at an advanced level, when the yogi finds absorption in awareness itself.
It is vital to understand that each of these three practices is distinct but essential. One cannot substitute the other, and the guidance for practicing each effectively is different too.