You can't know it is there
Unseen Servant creates (emphases mine):
an invisible, mindless, shapeless, Medium force that performs simple tasks at your command until the spell ends. The servant springs into existence in an unoccupied space on the ground within range.
As stated, the servant is invisible (meaning it cannot be seen) and is a force (meaning it cannot be touched). Although not explicitly stated, it is reasonable to assume that it also does not by itself produce taste, sound, or smell.
Typically detecting the presence of something (some thing) would be done with Perception (emphases mine):
Your Wisdom (Perception) check lets you spot, hear, or otherwise detect the presence of something. It measures your general awareness of your surroundings and the keenness of your senses. For example, you might try to hear a conversation through a closed door, eavesdrop under an open window, or hear monsters moving stealthily in the forest. Or you might try to spot things that are obscured or easy to miss, whether they are orcs lying in ambush on a road, thugs hiding in the shadows of an alley, or candlelight under a closed secret door.
Note the emphasis on using one's senses to detect the presence of things. Nothing in here implies that one might use Perception to detect the presence of a non-physical force.
[One might object that if the force truly has no physical presence, why then does it have a size, specified as Medium? I believe the intent here is both to clarify the part of the spell that says it must appear in an unoccupied space (that space being the size of a Medium creature, 5' square), and also setting a range for the size of objects it can manipulate - it would be able to hold up no more than a 5' section of rope, for example.]
Since it is a magical force, one might think it detectable by an Arcana check, but lo:
Your Intelligence (Arcana) check measures your ability to recall lore about spells, magic items, eldritch symbols, magical traditions, the planes of existence, and the inhabitants of those planes.
RAW, your Arcana functions for memory recall only, not as a limited 'detect magic' ability or some way to perceive mystic forces.
By their fruits ye shall know them
If there is no way to know that an unoccupied unseen servant is present, it is possible to deduce the presence of one through watching it work. That is the role of an Investigation check (emphasis mine):
When you look around for clues and make deductions based on those clues, you make an Intelligence (Investigation) check. You might deduce the location of a hidden object, discern from the appearance of a wound what kind of weapon dealt it, or determine the weakest point in a tunnel that could cause it to collapse.
When you see a bottle of wine being poured with no obvious support, you begin to make hypotheses - is it caused by an invisible being? Is it a mystical force? Is the whole thing an illusion? Watching the servant at its duties, seeing how it interacts with the world, will give you evidence to conclude what its nature is by means of a successful Investigation check, just as looking at a wound can tell you about the weapon that made it, even without seeing the weapon itself.
Differentiating from Mage Hand
Suppose you witness some invisible force pouring the contents of a wine bottle. Can you determine whether it is being caused by Unseen Servant or Mage Hand?
Can you see a hand?
Mage hand specifically says that the hand is "spectral" - so, ghostly and transparent but visible. To be fair, the OP specified an invisible mage hand, so perhaps one cast by an Arcane Trickster?
Is there a caster nearby? How close?
Mage hand vanishes if it is more than 30' from its caster, unseen servant ends if it is more than 60' from the caster. They are going to be close, but the mage hand caster will need to be closer.
What is the wine container like?
While the unseen servant can do things that require its force to be spread over a large area or have separate points of application (fold clothes, serve food), any application I have experienced of mage hand limits it to things that an actual, single hand could do, and the list of examples does not contradict this. I can remove the glass stopper of a wine decanter one handed and still pour it, but there is no way I could uncork a fresh bottle of wine with one hand. If your DM feels similarly, that would be an easy tell.
In the absence of these obvious signs, simply saying 'I look for any subtle evidence of the difference between the spells' should be enough to get you some kind of Investigation roll.