Learn English – the difference between seems like /seems that/seems

In terms of meaning, there is no difference between the second and third sentences.

It seems that they have not completed the task yet.

It seems they haven't completed the task yet.

The word that is not necessary to be there when it is used as a conjunction to introduce a subordinate clause expressing a statement or hypothesis.

I hope that I can fly.

I hope I can fly.

As suggested by RegDwighт♦, you can read more about it here.

If you care a lot about the details,

there is actually a very small difference between the first and second/third sentences.

It seems like they have not completed the task yet.

It seems (that) they have not completed the task yet.

The word like here is used as a preposition:

like

having the same characteristics or qualities as; similar to

and the interesting thing is, the word seem has the definition:

seem

give the impression or sensation of being something or having a particular quality

So when you use the second/third sentence

It seems (that) they have not completed the task yet.

you are giving a hypothesis as you are saying that

It gives an impression that they have not completed the task yet.

which shows that you are not totally sure if they have not completed the task.

Using the sentence with the word like would indicate that you are even less sure if they have not completed the task.

It gives an impression that is similar to that they have not completed the task.