The OmniSearch in Customer Care lets you search for Orders or Billing Orders. From either search results you can select an Order (or Billing Order) ID to display the Order Details.
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Order and Billing Order Search Options

Example, Order Search Results

Note
From the Billing Orders search results, clicking on a Billing Order ID takes you to the Billing Order Details in Customer Care. From the Orders search results, clicking on an Order ID takes you to the Order Details in the Orders web application.