Montaña vs. monte
The Spanish words 'montaña' and 'monte' both relate to elevated landforms, but they are used differently and have some contextual variations.
Montaña
A 'montaña' is a large, natural elevation of the earth's surface rising abruptly from the surrounding level; a mountain.
Los Alpes son una cadena de montañas en Europa.
(The Alps are a mountain range in Europe.)
Escalar una montaña requiere mucha preparación y condición física.
(Climbing a mountain requires a lot of preparation and physical condition.)
Las montañas suelen tener nieves perpetuas en sus cumbres.
(Mountains often have perpetual snow on their peaks.)
Monte
'Monte' can refer to a smaller elevation or hill, or more broadly it can mean natural, uncultivated land covered with vegetation. It is not necessarily as high or as distinct as a 'montaña'.
Cruzaron el monte para llegar al pueblo vecino más rápido.
(They crossed the hill to reach the neighboring town faster.)
El monte está lleno de vegetación espesa y diversa fauna.
(The wilderness is full of thick vegetation and diverse wildlife.)
Vivían cerca del monte donde corría un pequeño río.
(They lived near the wooded area where a small river ran.)
Summary
In summary, 'montaña' refers to larger, more distinct elevated landforms like mountains, while 'monte' can refer to smaller elevations (hills) or uncultivated natural areas.