die Welle
wave
A mass of water rising and moving along the surface of a body of water such as the sea or a lake.
Die Kinder sprangen lachend in die Wellen.
The children jumped laughing into the waves.

wave
Loading your saved state.
wave
A mass of water rising and moving along the surface of a body of water such as the sea or a lake.
Die Kinder sprangen lachend in die Wellen.
The children jumped laughing into the waves.

The basic meaning of the water wave is often used figuratively. A 'Welle' (wave) then describes a phenomenon that spreads quickly, like a wave in water. This helps you understand the different meanings.
Eine Grippewelle breitete sich im ganzen Land aus.
A wave of flu spread throughout the whole country.
When referring to water, 'Welle' (wave) is often combined with adjectives that describe its size or strength. Common phrases are 'hohe Wellen' (high waves), 'sanfte Wellen' (gentle waves), or 'riesige Wellen' (huge waves).
Trotz der hohen Wellen gingen die Surfer ins Wasser.
Despite the high waves, the surfers went into the water.
In the figurative meaning, 'Welle' (wave) often follows the structure 'eine Welle der/des + [abstract noun]' (a wave of + [abstract noun]). This creates fixed combinations such as 'eine Welle der Begeisterung' (a wave of enthusiasm), 'eine Welle der Gewalt' (a wave of violence), or 'eine Welle der Hilfsbereitschaft' (a wave of helpfulness).
Der Sieg der Mannschaft löste eine Welle der Begeisterung aus.
The team's victory triggered a wave of enthusiasm.
You can recognize this meaning from the technical or scientific context. Signal words here are 'Radio' (radio), 'Schall' (sound), 'Licht' (light), 'Frequenz' (frequency), or verbs like 'senden' (to broadcast/transmit) and 'empfangen' (to receive).
Schall breitet sich in Wellen aus.
Sound spreads in waves.
This very specific meaning occurs only in technical contexts. You can recognize it from words like 'Motor' (engine), 'Getriebe' (transmission), 'Maschine' (machine), 'Achse' (axle), or 'Mechaniker' (mechanic).
Die Welle im Motor war gebrochen und musste ersetzt werden.
The shaft in the engine was broken and had to be replaced.
axis / axle
'die Welle' and 'die Achse' can both refer in technology to a rod or component in a machine. That is why they are easy to confuse. An 'Achse' often supports or connects wheels, for example on a bicycle or car. A 'Welle' mainly transmits rotational motion from one part of a machine to another. In some simple situations, the parts look similar. More precisely, though: with wheels, people often speak of an 'Achse'; when force or rotation is being passed on, 'Welle' is usually the more suitable word.

Nach der Arbeit prüft der Mechaniker die Welle, weil der Motor stark vibriert.
After work, the mechanic checks the shaft because the engine is vibrating strongly.
In der Werkstatt wird die verbogene Achse des Anhängers ausgetauscht.
In the workshop, the bent axle of the trailer is being replaced.