No. The Online versions are different. Only 1 return per account. And several other differences and the price structure is different. There is no Forms mode. And you may have to use a higher online version to enter something. In the Desktop program all the versions have the same forms.
When you use Online TurboTax, you get one return per fee. Each return needs its own account and user ID. If you use the same account and user ID for a second return, you overwrite the first one and lose it forever.
When you use Desktop TurboTax, which you install from a CD or download to your own hard drive, you can prepare and e-file multiple returns for the cost of the software. You can e-file up to 5 Federal returns—more if you mail the additional ones. If you have multiple returns to prepare for family members, Desktop is more cost effective.