zart
tender
Soft and easy to chew or cut, especially with foods such as meat.
Das Steak war unglaublich zart und saftig.
The steak was incredibly tender and juicy.

tender / delicate
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tender
Soft and easy to chew or cut, especially with foods such as meat.
Das Steak war unglaublich zart und saftig.
The steak was incredibly tender and juicy.

You can recognize the exact meaning of 'zart' (tender/delicate) from the noun it describes. Depending on whether it refers to food, a color, a person, or an object, the meaning changes.
Das zarte Gemüse war schnell gar.
The tender vegetables were cooked quickly.
When referring to food, 'zart' (tender) is often used to describe soft meat or vegetables. Typical combinations are 'zartes Fleisch' (tender meat), 'zartes Gemüse' (tender vegetables), or 'zarter Fisch' (tender fish).
Das Lammfilet war so zart, dass es auf der Zunge zerging.
The lamb fillet was so tender that it melted on the tongue.
When something is described as 'zart' (delicate) in the sense of fragile, typical nouns are 'Pflanze' (plant), 'Haut' (skin), 'Seele' (soul), or 'Glas' (glass).
Die zarte Haut eines Babys braucht besonderen Schutz.
A baby's delicate skin needs special protection.
To describe a gentle or loving action, 'zart' (gentle) is often combined with words such as 'Berührung' (touch), 'Kuss' (kiss), or 'Stimme' (voice).
Mit einer zarten Bewegung strich er ihr eine Haarsträhne aus dem Gesicht.
With a gentle movement, he brushed a strand of hair out of her face.
In combination with a color, 'zart' (soft) describes a light, unobtrusive pastel shade. For example, people say 'ein zartes Grün' (a soft green) or 'ein zartes Gelb' (a soft yellow).
Für das Kinderzimmer wählten sie zarte Pastellfarben.
For the children's room, they chose soft pastel colors.
Describing a young age with 'zart' (tender) is rather elevated or poetic. It is almost always used in the fixed expression 'in zartem Alter' (at a tender age).
Er lernte schon in zartem Alter das Klavierspielen.
He learned to play the piano at a tender age.
fine
'fein' and 'zart' overlap when something seems light, thin, pleasant, or not coarse. 'zart' especially emphasizes softness, sensitivity, or gentleness, for example with skin, flowers, colors, or meat. 'fein' can also mean very small, precisely made, or elegant, as with fabric, sand, or workmanship. The words can be confused because both describe something non-coarse. In practical terms: 'zart' is more suitable when something is soft or delicate; 'fein' is more suitable when something is very thin, precise, or elegant.

In der Vase stehen zarte Blumen, die schnell welken.
There are delicate flowers in the vase, and they wilt quickly.
Der feine Sand bleibt nach dem Strandbesuch in den Schuhen.
The fine sand stays in your shoes after a visit to the beach.