We can perceive something “out there,” such as a rainbow that we experience through our senses. If we are color-blind, that rainbow looks different to us than if we see in full color. If we are tone-deaf a symphony may be just so much rhythmic noise. If we have a highly tuned sense of hearing, we can hear all the musical variations and be touched emotionally.
Perception and the physical senses are inter-related. It relies on such senses as sight, hearing, touch, taste, and smell.
Awareness comes from inside and does not rely on the physical senses. A blind person may not see the rainbow but can be aware that a rainbow exists because people have told him or her about it. Or they can hear people exclaiming with wonder at the beauty of the rainbow and therefore they know that rainbows are perceived to be beautiful.
Awareness is in the background. Perception is in the foreground. And like perception, awareness varies according to the individual. Though it does not rely on the senses, some people have more finely-tuned awareness than others. They feel and recognize the being that does the perceiving. Helen Keller was a great example of this. She was blind and deaf but still was aware of the person or soul she was inside.
There are degrees of awareness. Some people go through life like living zombies, on automatic pilot. Others are highly attuned to their inner and outer environment (regardless of the condition of their physical senses). But awareness does not depend on whether something exists out there or not. It is a mental and spiritual thing.