What is the difference between seems like /seems that/seems?

Is there any difference between these expressions?

It seems like they have not completed the task yet.

It seems that they have not completed the task yet.

It seems they haven't completed the task yet.

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.

Seem is a very odd verb, and participates in a number of odd constructions.

First, notice that seem means the same as (and has much the same syntax as) appear, which is a visual sense verb that's been generalized to all senses. Seem has been bleached of most of its verbal meaning, and now is merely used to add a touch of dubiosity to a judgement, like an adverb or a modal.

• They're rioting in Africa.
• They seem to be rioting in Africa.
• Possibly they are rioting in Africa.
• It's cold out.
• It appears to be cold out.
• It might be cold out.

The syntax of seem, however, is a mare's nest, and it's an old mare.

Seem originally meant think, and in Middle English dialects both had cliticized first person dative-subject constructions marking the experiencer subject as me:

• Methinks the truth should live from age to age. (Richard III: III.i)
• Mee seemes hee makes it something more excellent then Faith it self (Sclater, 1629)

But as the Dative Subject construction died out in English, think and seem moved in different syntactic directions, and today they don't behave at all similarly.

Think became a stative transitive verb with experiencer subject in the nominative, not the dative, taking a tensed that-complement object.

• I think that I shall never see a poem lovely as a tree.

Seem, on the other hand, became a intransitive flip verb with the experienced phenomenon as the subject, not the object; and a deletable dative experiencer, expressed if necessary as a prepositional phrase with to. It thus takes a subject complement, not object.

• That I shall never see a poem lovely as a tree seems (to me).

Of course, this is a terrible sentence because the verb, which means practically nothing, is the last word in the sentence (since to me is usually understood), in the place where the most important word belongs. English fixes this by extraposing the whole subject clause at the cost of leaving behind a dummy it subject.

• It seems (to me) that I shall never see a poem lovely as a tree .

Seem, however, unlike think, can also take infinitive complements, and that's where A-Raising comes in. The awkward but grammatical sentences

• [For it to be raining|For there to be a unicorn in the garden] seems (to me).
• [For them to be tired|For him to be ready to go] seems (to me).

get transformed by A-Raising into the much more palatable

• It seems to be raining | There seems to be a unicorn in the garden.
• They seem to be tired | He seems to be ready to go.

Seems like is just a variant on seems, and that is just a complementizer for the tensed complement.