dürr
gaunt
Refers to a person or animal that is very thin or skinny, often in an unhealthy way.
Das alte Pferd war ganz dürr und schwach.
The old horse was completely gaunt and weak.

gaunt / withered / sparse
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gaunt
Refers to a person or animal that is very thin or skinny, often in an unhealthy way.
Das alte Pferd war ganz dürr und schwach.
The old horse was completely gaunt and weak.

The adjective 'dürr' (gaunt / withered / sparse) is closely related to the noun 'die Dürre' (drought), which describes a long period without rain. Both words share the basic meaning of dryness and lack.
Wegen der langen Dürre ist das Gras auf den Feldern ganz dürr.
Because of the long drought, the grass in the fields is completely withered.
The meaning of 'dürr' (gaunt / withered / sparse) becomes clear from the noun it describes. If it refers to a person, it means 'mager' (skinny/gaunt). If it refers to plants, it means 'vertrocknet' (withered/dried out). If it refers to words, it means 'karg' (sparse/bare).
Der Läufer war groß und dürr.
The runner was tall and gaunt.
When 'dürr' (gaunt) describes a person, it often has a negative connotation and means 'ungesund mager' (unhealthily thin) or 'knochig' (bony). It is stronger and more negative than 'dünn' (thin) or 'schlank' (slim).
Nach seiner langen Krankheit war er sehr blass und dürr.
After his long illness, he was very pale and gaunt.
In the meaning 'vertrocknet' (withered/dried out), 'dürr' (withered) is often combined with parts of plants or landscapes. Typical examples are 'dürre Äste' (withered branches), 'dürres Gras' (withered grass), or 'dürre Zweige' (withered twigs).
Das Feuer breitete sich im dürren Unterholz rasend schnell aus.
The fire spread incredibly quickly through the dry undergrowth.
In its figurative meaning, 'dürr' (sparse) is often used for communication that lacks details or emotion. Typical examples are 'dürre Worte' (sparse words), 'eine dürre Mitteilung' (a terse message), or 'eine dürre Zusammenfassung' (a sparse summary).
Er beantwortete meine Frage nur mit ein paar dürren Worten.
He answered my question only with a few sparse words.
dry
'trocken' and 'dürr' can both describe a lack of water. 'trocken' is the more general word: a towel, a floor, or the air can be 'trocken'. 'dürr' is stronger and is used mainly for plants or landscapes that have dried out because of too little water and are often damaged. In a figurative sense, both can also describe something bare or lacking life. Learners should be careful, though: for normal objects, you usually say 'trocken', not 'dürr'. 'dürr' can also describe people or animals as very thin; 'trocken' cannot do that.

Nach dem heißen Sommer standen nur noch dürre Pflanzen im Garten.
After the hot summer, only withered plants were left standing in the garden.
Nach einer Stunde in der Sonne war die Wäsche wieder trocken.
After an hour in the sun, the laundry was dry again.