Absence of evidence is not evidence of absence?

The absence of evidence is the lack of any kind of evidence.

Evidence of absence refers to actively looking for any kind of evidence and such evidence can be used to infer or deduce the non-existence of something.

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For example, if a doctor cannot find malignant cells in a patient, this null result is the evidence of absence of cancer. The absence of malignant cell is the evidence of absence of cancer.

Or, the absence of perceiving Santa Claus is the evidence of the absence of Santa Claus.

Or, the absence of perceiving God is the evidence of the absence of God. Is it?