When we are trying to make a specification, we rely on phrases like "sort of," "type of," and "variety of." You may think these words each correspond with the most similar word in the title above, but things are not that simple. This is German, after all!

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Die Art can be most generically employed as a translation for "the type of" or "the sort of," and also "the way of." 

Spätzle sind eine Art bayrische Nudeln.

Spaetzle are a type of Bavarian noodle.

Caption 2, Bayrische Spätzle - mit Christiane

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Es gibt verschiedene Arten von Wind:

There are various types of wind:

den säuselnden Hauch,

the murmuring breath,

die leichte, die frische und die steife Brise...

the light, the fresh and the stiff breeze...

Captions 10-12, Piggeldy und Frederick - Der Wind

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Die Art also can refer to someone's personality, as in their way of being or way of behaving, and it also can refer to a species of animal. 

Es ist überhaupt nicht ihre Art, einfach so wegzulaufen.

It's not her nature to simply run away like that.

Caption 33, Großstadtrevier - Von Monstern und Mördern

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Einige Tierarten aber

Some animal species, however,

machten sich die gewaltige Umgestaltung der Küste zunutze.

have made use of the enormous transformation of the coast.

Caption 5, Abenteuer Nordsee - Unter Riesenhaien und Tintenfischen

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Die Sorte is quite similar to die Art, but will more likely be employed for things that are in some way man-made. For example, if you are talking about a variety or flavor of food, often one that is specified by a name, you generally will use die Sorte rather than die Art. 

Die Sorte „Jamaika Blue Mountain“,

The variety "Jamaica Blue Mountain,"

quasi der Champagner unter den Kaffees,

quasi the champagne of coffees,

kostet sogar über zwanzigmal so viel

even costs over twenty times as much

wie ein Kaffee aus dem Supermarktregal.

as a coffee from the supermarket shelf.

Captions 14-17, Kaffee - Noch von Hand gemacht

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Die Eissorten werden jedes Jahr exotischer.

The ice-cream flavors get more exotic every year.

Caption 2, Eis - Eiskalte Leidenschaft

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Der Typ is a bit trickier, as it is not universally used to mean "type" like in English. In fact, it is most often used as a slang expression to simply mean "the guy." But it can also mean "type of guy." Like in English, you can say Er/Sie ist nicht mein Typ, which means that the person doesn't interest you romantically. 

Ich bin ein sehr nachdenklicher Typ und Mensch.

I am a very thoughtful guy and human being.

Caption 16, Andreas Bourani - Startet durch

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Er war schon immer so ein Typ, dem alles so zufliegt.

He was always the kind of guy who always gets everything.

Captions 22-23, Joris - Er

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Further Learning
Keep an eye out for examples with these words used on Yabla German, and always look at the noun in the sentence. You will notice patterns which can help you choose the right option later on.