die Schnur
string / cord
A thin, long, and flexible object made of twisted fibers that is used for tying, fastening, or hanging things.
Sie band das Paket mit einer dicken Schnur zu.
She tied up the package with a thick string.

cord / string
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string / cord
A thin, long, and flexible object made of twisted fibers that is used for tying, fastening, or hanging things.
Sie band das Paket mit einer dicken Schnur zu.
She tied up the package with a thick string.

The meaning depends heavily on the context. If it's about tying, crafts, or hanging things up, a normal string or cord is meant. In connection with electrical devices such as a vacuum cleaner or lamp, 'Schnur' (cord) colloquially refers to the power cable.
Gib mir bitte die Schnur, ich möchte das Geschenk verpacken.
Please give me the string; I want to wrap the gift.
In the general meaning, 'Schnur' (string/cord) is often used with verbs such as 'binden' (to tie), 'befestigen' (to fasten), 'zuziehen' (to pull tight), or 'aufwickeln' (to wind up). For example, people speak of a 'Wäscheleine' (clothesline, a cord for laundry) or a 'Paketschnur' (parcel string).
Er band die losen Blätter mit einer Schnur zusammen.
He tied the loose sheets together with a string.
Using 'Schnur' (cord) for a power cable is rather colloquial. In technical or more formal contexts, you would use the word 'Kabel' (cable).
Zieh bitte die Schnur aus der Steckdose.
Please pull the cord out of the outlet.
The idiom 'wie am Schnürchen laufen' (to run smoothly) is a fixed unit. The subject of the sentence is always the process or event that is functioning smoothly.
Die Vorbereitung für das Fest ist wie am Schnürchen gelaufen.
The preparation for the festival ran smoothly.
ribbon / band
'das Band' and 'die Schnur' can both be long, narrow things used to tie or fasten something. The important difference is in the shape and material: a 'Band' is usually flat and often a bit wider, for example made of fabric or plastic. A 'Schnur' is usually round, thin, and flexible, often made of twisted fibers. They can be confused because both are used for tying things together. If something is flat like a strip, 'Band' fits better. If it is thin and thread-like, 'Schnur' sounds more natural.

Im Garten hängt Max die Lampe an einer langen Schnur auf.
In the garden, Max hangs the lamp from a long cord.
Lisa bindet ein rotes Band um das Geschenk.
Lisa ties a red ribbon around the gift.