How to store the value in rule input if value and saveInto are not having same values.

2 things:

1. for a simple SaveInto, you don't need to use a!save() unless you're trying to save a value different from the value parameter of the component.  In other words, here you could just type "saveInto: ri!monitoringDetails.monitoringDay"
2. I see you have "readOnly" set to a value of true.  This means no user interaction will be possible on this text field, meaning that nothing in the saveInto parameter will ever execute.  Can you tell us a bit more about the use case that you would be trying to use this for?

As per the use case , If I enter the monitoringDate it should automatically display and save day corresponding to that date in rule input as read only field:

If the user input is happening in the Monitoring Date field, then the saveInto will need to happen there.  This is where we end up needing a!save, it makes our job very easy:

a!dateTimeField(
  label: "Monitoring Date",
  labelPosition: "ABOVE",
  value: ri!monitoringDate,
  saveInto: {
    ri!monitoringDate,
    a!save(
      ri!monitoringDetails.monitoringDay,
      text(save!value, "dddd"),
    )
  },
  required: true,
  readOnly: false,
  validations: {}
),

a!textField(
  label: "Monitoring Day",
  labelPosition: "ABOVE",
  value: ri!monitoringDetails.monitoringDay,
  showWhen: not(isnull(ri!monitoringDate)),
  required: false,
  readOnly: true
),

If the user input is happening in the Monitoring Date field, then the saveInto will need to happen there.  This is where we end up needing a!save, it makes our job very easy:

a!dateTimeField(
  label: "Monitoring Date",
  labelPosition: "ABOVE",
  value: ri!monitoringDate,
  saveInto: {
    ri!monitoringDate,
    a!save(
      ri!monitoringDetails.monitoringDay,
      text(save!value, "dddd"),
    )
  },
  required: true,
  readOnly: false,
  validations: {}
),

a!textField(
  label: "Monitoring Day",
  labelPosition: "ABOVE",
  value: ri!monitoringDetails.monitoringDay,
  showWhen: not(isnull(ri!monitoringDate)),
  required: false,
  readOnly: true
),

Thank you so much Mike for providing one more feasible solution.

Great, thanks for confirming.  If and when you're willing, it would be helpful if you could click "verify" on any of my answers that you found helpful, and other peoples' answers too.  I believe this will turn the answers "green" and mark the thread as "resolved".  It also gives some invisible "brownie points" to the verified answer-giver ;-)