unten
down / below
Indicates a position or place that is on a deeper or lower level.
Die Gläser stehen im Schrank ganz unten.
The glasses are at the very bottom of the cupboard.

down / below
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down / below
Indicates a position or place that is on a deeper or lower level.
Die Gläser stehen im Schrank ganz unten.
The glasses are at the very bottom of the cupboard.

The adverb 'unten' (down/below) always describes a static position, that is, a place where something is located. It answers the question 'Wo?' (Where?). It is not used for movement downward.
Wo ist mein Handy? – Es liegt da unten auf dem Tisch.
Where is my phone? – It's down there on the table.
'Unten' (down/below) is an adverb and often stands alone or at the end of a sentence. It does not need a noun. Don't confuse it with prepositions, which describe a relationship between two things and require a noun in the correct case.
Die Katze ist nicht hier oben, sie muss unten sein.
The cat isn't up here; it must be downstairs.
The context makes it clear whether 'unten' (down/below) means a physical place or a point in a document. In combination with words like 'Seite' (page), 'Text' (text), 'Liste' (list), or 'Link' (link), it refers to the document.
Die genauen Quellen sind unten im Text verlinkt.
The exact sources are linked below in the text.
The idiom 'bei jemandem unten durch sein' (to be in someone's bad books) is a fixed unit. It means that you have lost that person's sympathy or trust. The person whose favor you have fallen out of is used with the preposition 'bei'.
Nach dieser Lüge ist er bei seinen Freunden komplett unten durch.
After that lie, he's completely in his friends' bad books.
under
'unter' and 'unten' both describe a lower position. The difference is grammar: 'unter' is a preposition and normally needs a reference word, for example 'unter dem Tisch' (under the table). 'unten' is an adverb and only names the place on a lower level, for example 'unten im Haus' (downstairs in the house). Learners easily confuse them because the spatial idea is similar. Ask yourself: Is there an object that something is under? Then use 'unter'. Do you just mean the lower place? Then 'unten' fits.

Unten im Krankenhaus wartet ein Freund auf uns.
Downstairs in the hospital, a friend is waiting for us.
Im Restaurant liegt ihre Tasche unter dem Stuhl.
In the restaurant, her bag is under the chair.