Is a 1095-B the same thing as a 1095-A?

NO.  A Form 1095-B is Not the same as a Form 1095-A.  A Form 1095-B is not entered on a tax return.

No. The 1095A is for those who purchased subsidized health insurance via the Marketplace.

The 1095B indicates coverage from employer. 
The 1095A needs to be reported on tax return. 
1095B does not need to be reported on tax return.

Form 1095-A is provided to you when you have health insurance through a health care exchange. The information is entered on your tax return to reconcile tax credit payments and claim any premium tax credits that may be due to you.

Form 1095-B is issued to members of health insurance plans as a verification of Minimum Essential Coverage (MEC). You don't have to enter the information on your tax return. Some states may ask if you have Minimum Essential Coverage, which this form verifies the time that you had the coverage.

For additional information, review the TurboTax article What are 1095 Tax Forms for Health Care? And IRS FAQs about Health Care forms.