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.
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.
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.
The word like here is used as a preposition:
and the interesting thing is, the word seem has the definition:
So when you use the second/third sentence
you are giving a hypothesis as you are saying that
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.
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.
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:
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.
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.
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.
Seem, however, unlike think, can also take infinitive complements, and that's where A-Raising comes in. The awkward but grammatical sentences
get transformed by A-Raising into the much more palatable
Seems like is just a variant on seems, and that is just a complementizer for the tensed complement.