Any assertion about the truth or untruth of a proposition may be called a "claim".
George claims that the Vikings discovered America.
Angela claims that Meryl Streep is the best living film actor.
Darcy claims that the Republicans will win the presidency next year.
But only an assertion about future eventualities may be called a "prediction". Darcy's claim is a prediction, but George's claim and Angela's claim are not.
Note that future is to be understood here in relation to the time when the prediction is uttered. The internet has been around for a quarter-century, but it is still proper for me to say:
Nicolas Tesla predicted the internet.
—because Tesla made this prediction in 1900.
Note, too, that predict is often in the sciences to speak of what appears to be mere correlation. A sociologist, for instance, may write:
Education is a strong predictor of poverty.
This is a figurative use. What the sociologist means is that if you divide a population into groups by how much education the individuals in each group has, you may "predict" with some accuracy how many poor people will be found in each group—a hypothetical future event.
Your example involves a claim about the future: the number of new jobs created this year will fall short of last year's record. This claim is a prediction.
No, they do not mean the same thing. Not only does around make the second sentence grammatical, but the use of for in the first sentence gives that sentence a different meaning.
He has failed the exam for the first time.
He may have written the exam five times before. But this time, the sixth time, he has failed it. It is the first time that he has failed it.
He has failed the exam the first time around.
This means that it's the first time he's written the exam—and that he's failed it.
The sentence construction is a bit odd, but it works if you think of somebody announcing the result immediately after the attempt—and just before he attempts it a second time.
Note the difference that around makes in variations of the sentence:
✔ He has failed the exam the first time around.
✘ He has failed the exam the first time.
✔ He failed the exam the first time around.
✔ He failed the exam the first time.
In the has failed version, the sentence becomes ungrammatical if you simply remove around. However, I can't really explain why this is the case.
The final version without around seems correct, but it is also awkward; I would add he wrote it to the end.
Best Answer
In these sentences the two verbs are completely interchangeable. There is no significant difference.
Elsewhere there would be differences, of course. Animate objects tend to grow and inanimate objects tend to expand, for instance. Even in those usages there are often cases where the two verbs could be swapped.