Mindfulness is present-time awareness. It takes place in the here and now. It is the observance of what is happening right now, in the present moment. It stays forever in the present, perpetually on the crest of the ongoing wave of passing time.
If you are remembering your second-grade teacher, that is memory. When you then become aware that you are remembering your second-grade teacher, that is mindfulness. If you then conceptualize that process and say to yourself, "Oh, I am remembering," that is thinking.