Why does `default( None )` not always appear to produce `None`

Is there a logical reasoning that explains why the two debug tasks in the Ansible playbook below respectively output "NONE" and "FALSE" and not both "NONE"?

- hosts:  'all'

  tasks:

    - debug:
        msg: '{{ foo | default( None ) | ternary( "TRUE", "FALSE", "NONE" ) }}'

    - debug:
        msg: '{{ bar | ternary( "TRUE", "FALSE", "NONE" ) }}'

  vars:

    bar: '{{ foo | default( None ) }}'

I observed this with ansible@2.8.5 btw

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[edit@2019-10-16]

As inferred from @VladimirBotka's answer, one could say the real "problem" is that None isn't transitive with respect to substitution. My use of default(...) was needlessly complicating matters and the example can be simplified to:

- hosts: 'all'
  tasks:
    - debug:
        msg: '{{ None | ternary( "TRUE", "FALSE", "NONE" ) }}'

    - debug:
        msg: '{{ bar | ternary( "TRUE", "FALSE", "NONE" ) }}'

  vars:
    bar: '{{ None }}'

... and still produce the exact same output.

• foo | default(None) evaluates to null
• {{ foo | default(None) }} evaluates to an empty string ""

---

^{Note: All Jinja expressions closed in double braces {{ expression }} evaluate to strings.}

---

Given

  bar: "{{ foo | default(None) }}"

the task

  - debug:
      msg: bar is empty string
    when: bar | length == 0

gives

  msg: bar is empty string

But the task

  - debug:
      msg: foo is empty string
    when: foo | default(None) | length == 0

fails with the error:

"... object of type 'NoneType' has no len() ... "

As a result in ternary, an empty string selects FALSE and null selects NONE.

---

Notes:

1. See the Note in Omitting Parameters

2. Both null and empty string "" select FALSE in ternary if the third parameter is omitted. The tasks

  - debug:
      msg: "{{ bar | ternary('TRUE', 'FALSE') }}"
  - debug:
      msg: "{{ foo | default(None) | ternary('TRUE', 'FALSE') }}"

give

  msg: FALSE
  msg: FALSE