QB Issue Resolution:

they are NOT interchangeable, it is one or the other but not both

how to go from QBO to QBDT
http://support.quickbooks.intuit.com/support/articles/HOW12246

the export to desktop provides you with a file that must be opened in desktop within 10 days, and the file has known problems, some things do not export, inventory exports as service items with no history, these known problems have existed for over 5 years
https://qboe.custhelp.com/app/answers/detail/a_id/1447

Resolution for Issue 'just purchased the 2015 desktop pro version and would like to export my data from my online version. are they interchangable and can I use them both at the same time?' available: Yes (Solved).
Source: Intuit Community forum.

just purchased the 2015 desktop pro version and would like to export my data from my online version. are they interchangable and can I use them both at the same time?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for Desktop
Quickbooks Repair Pro will resolve it efficiently and affordably. Guaranteed resolution of your issue, or you pay nothing!

Error Recovery for Desktop [Canada]
E-Tech is the #1 Quickbooks data migration and Conversion service provider.

Get 50% off Quickbooks Online

Click Here for 50% off!

Additional Support Options: