What is the difference between the following two sentences?

The second sentence is grammatically incorrect.

Per Merriam-Webster:

test (verb)
tested; testing; tests

transitive verb

  1: to put to test or proof : TRY —often used with out
  2: to require a doctrinal oath of 

intransitive verb

  1:
    a: to undergo a test
    b: to be assigned a standing or evaluation on the basis of tests 
         tested positive for cocaine
         the cake tested done

  2: to apply a test as a means of analysis or diagnosis —used with for
      test for mechanical aptitude

In the first sentence, it's definition 1b of the intransitive verb that applies. This is because O'Brien is not testing a direction object; the verb test is being used intransitively to say that he has been "assigned an evaluation, on the basis of tests, of being positive for coronavirus"

The second sentence is in the passive voice. In this instance, O'Brien is the direct object of the verb test. However, there are no versions of test as a transitive verb that would then make sense.

If you constructed the sentence yourself, then you can dismiss it as just incorrect. If you, in fact, read it in some reporting, then it's either an error, or it could possibly be a contraction of a valid sentence, such as:

White house national security adviser Robert O'Brien has been tested [and found to be] positive for Covid-1, a senior administration official says.

Some outlets take liberties with English grammar to save column inches.