Durazno vs. melocotón

The Spanish words "durazno" and "melocotón" both mean "peach" in English. The distinction between them lies primarily in their regional usage.

Durazno

'Durazno' refers to a peach and it is widely used in many Latin American countries such as Mexico, Peru, Argentina, Chile, and Uruguay. It's derived from the Latin word 'dūrus acinus', which literally translates to 'hard seed'.
El durazno es mi fruta favorita en el verano.
(The peach is my favorite fruit in the summer.)
¿Puedes agregar algunos duraznos a la ensalada de frutas?
(Can you add some peaches to the fruit salad?)
El pastel de durazno es un postre popular en Argentina.
(Peach pie is a popular dessert in Argentina.)

Melocotón

'Melocotón' also signifies a peach but it is commonly used in Spain. This term stems from its old name 'mālum cotōnium' which meant 'quince apple'.
El melocotón es una fruta jugosa y dulce.
(The peach is a juicy and sweet fruit.)
En España, el zumo de melocotón es muy popular.
(In Spain, peach juice is very popular.)
Este batido se hizo con melocotones frescos.
(This smoothie was made with fresh peaches.)

Summary

To summarise, both 'durazno' and 'melocotón' refer to the same fruit – peach, but their usage varies across different Spanish-speaking countries. 'Durazno' is behind common usage in Latin America, while 'melocotón' is more commonly used in Spain.