The 'thinking I am' is the Jungian ego/Ahamaka at work, it consists of all those 'contents' that we identify and/or associate with as being what we consist of. Such as "I am Spiritual, enlightened, clever......" Associating/identifying with "I am" as a Spiritual concept/ideology or an escape is status as far as the ego is concerned. The ego makes no distinction between status in a context of money or perceptual Spiritual understanding, so as far as the ego is concerned "I am rich" and "I am oh so Spiritual" is the "thinking I am" or what the ego perceives itself to consist of. The "heart I am" - depending on how you personally experience it - is beyond ego because there is no thinking involved - it's beyond the brain/mind/ego mechanism. It is a feeling beyond feeling or Gnosis/knowing, consciousness..... and is a 'pure' personal source/core I Am. It's the difference between "I am" and "I am enlightened/Spiritual."