- The baby seems happy/comfortable.
- The baby seems to be happy/comfortable.
Are these both correct? If both are correct, what are the differences between them?
Seem used as a link verb can be followed by an adjective,to be +an adjective,
You seem (to be )angry with something,
She seems (to be) a nice girl.
They seem to have made a mistake.
The village seems (like) a nice place for a holiday.
that- and if-clauses.
It seems as if the night is never going to end.
With there seem(s) to be is used.
There seem to be a lot of mistakes.There seems to be some problem.
Seem and seem to be are interchangeable in most cases and the difference is not always clear-cut. It often depends on whether we are mentioning objective facts or expressing our subjective ideas.It depends on what you want to say.
The bus seems to be full.(It is true. It really is. ).
According to the experts, the building seems to be one hundred years old.(We trust the experts).
It seems crazy,but I think I am in love with him.(My subjective impression)
She seems sleepy.(I think so.)
She seems to be sleepy. (Look at her!)
STRAIGHT TO THE POINT - SHORT ANSWER -
The baby seems happy/comfortable.
The baby seems to be happy/comfortable.
They both are correct, and there is no difference in meaning.
DIGGING DEEPER - EXPLANATION -
We will discuss here this structure - X copular verb Y.
At this very beginning we will discuss two types of Copular Clauses - one is Ascriptive and the other is Specifying.
1. Sam [THEME] was hungry [PROPERTY].
2. Robin [VARIABLE] was the tallest of them [VALUE].
In Ascriptive use, as in sentence #1 the Predicative Complement (PC) ascribes the property or the characteristics of the subject. On the other hand in the Specifying use, as in sentence #2, the PC helps to specify or identify the subject.
At times they are ambiguous, that means they can be explained both as Ascriptive use and Specifying use.
The victim is Kim's sister.
In specifying use, the victim is identified as Kim's sister. In ascriptive use, it only says the victim is the sister of Kim, now imagine that Kim has more than one sister,it doesn't say which sister of Kim is the victim. So it's in that situation an ascriptive use. (In specifying use it implies that Kim has only one sister.)
The verb - be - can license both ascriptive PC and specifying PC, whereas other copular verbs can license only the ascriptive PC. If other copular verbs license to-infinitive clause the limitation can be overcome with the use of to be before a Specifying PC.
It was Max. [The verb - be - can take a specifying PC]
!It seemed Max [INCORRECT - because the copular verb - seem - can't take a specifying PC]
And it can be overcome with the use of to be -
It seemed to be Max.
But the use of to be after seem is not restricted to only the situation where we need a specifying PC. As seem can license a to-infinitive, we can use optional to be even before an ascriptive PC. But notice the difference, in the ascriptive use, the use of to be is optional, but in case of specifying use the use of to be is obligatory.
In OP's examples the AdjPs - happy or comfortable - denotes a property, and nothing but Ascriptive PCs in those sentences. So the use of to be after the verb - seem - is optional.
Now that we know when to use to be after seem optionally and when to use it obligatorily, let's focus on what extra meaning to be adds, if at all.
Most of the times there is no difference in meaning between seem to be and seem, but seem to be is preferred when we mean something that appears to be definitely true (objective facts). On the other hand seem without to be is preferred when it's based on personal feeling (subjective impression).
For example -
The doctors have done all the tests, and he definitely seems to be insane.
It seems insane, but I think I'm in love with the postman. [NOT
It seems to be insane]
The boy seems (to be) happy/comfortable
When you use the word 'seem' as a linking verb (copular) followed by a gradable adjective, say happy or comfortable, you can use the 'seem' with or without 'to be', without any difference in meaning.
You can also use the verb seem with or without 'to be' when it's followed by a noun phrase having an adjective such as:
He seems (to be) a nice man.
The use of the seem without to be is more common in the cases stated above.
However, you use to be after seem when a noun phrase follows a determiner without an adjective, for example:
He seems to be the owner of this house.
As for non gradable adjectives such as asleep, alone, alive, etc., you usually use 'to be" after 'seem'. For example:
He seems to be asleep.
Besides, you use 'to be' after the 'seem' when it's followed by an -ing form. For example:
He seems to be having breakfast at the moment.
However, you don't use to be when the seem is followed by a clause with that, like, or as if/as though. For examples:
It seems (that) he'll go to London tomorrow.
It seems like you are catching a cold.
It seems as if/as though you don't have enough money.
This question is more intricate than it seems...
"Seem" is one of the copular or linking verbs, which can be used in the same way as the verb "be" (actually "be" is part of this family too). So "the baby is happy", "the baby seems happy", but "the baby smiles happily" ("smile" is not a linking verb). A longer discussion can be found here.
But "seem" is a special copular verb, since it can also be used with "to be" with almost the same meaning; the only other copular verb that can be used this way is (or seems to be) "appear". So, just explaining copular verbs might not tell you the whole story.
Both "seem" and "appear", when used as copulae, suggest an uncertain opinion or observation; they are very useful for discussing something you aren't sure about (as I am doing now!).
Looking at the sentences you provide as example, there seems to be (that is, I think there is) a subtle difference:
The baby seems happy
I read it as "the baby looks happy [to me]"; it suggests a neutral observation, impression or interpretation of how the baby looks - it might be wrong, but it is definitely the speaker's observation.
The baby seems to be happy
I read this as "the baby looks as if he/she is happy [but I suspect that it's not true]"; it suggests some doubt in the speaker's mind - it is more an opinion than an observation.
You can also consider "it seems to be" as a passive way of saying "I think it is"; for example, "John seems to be missing" practically means "I think John is missing" (if John is not present, then saying "he seems missing" doesn't make much sense).
There are cases where the distinction is difficult, since people often state their observations as opinions (as a way of being polite); so you may hear people say "there seems to be a problem...", when they actually mean "there is definitely a problem". Nevertheless, I think this "observation vs. opinion" or "neutrality vs. doubt" is the key to deciding which form to use.
"seems to be happy" is the original formula. "to be" is mostly dropped because "to be" does not achieve much.