strahlen
shine
To emit light or heat. Often used for celestial bodies or lamps.
Die Sonne strahlte den ganzen Tag vom Himmel.
The sun shone in the sky all day.

to shine / radiate
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shine
To emit light or heat. Often used for celestial bodies or lamps.
Die Sonne strahlte den ganzen Tag vom Himmel.
The sun shone in the sky all day.

The verb 'strahlen' is directly related to the noun 'der Strahl' (for example, a ray of light). So something that 'strahlt' emits rays.
Ein heller Strahl Licht fiel durch das Fenster.
A bright ray of light fell through the window.
The meaning of 'strahlen' depends strongly on the subject. When celestial bodies or lamps are the subject, the literal meaning 'to emit light' is intended. When a person is the subject, the figurative meaning 'to glow with joy' is usually intended.
Die Scheinwerfer des Autos strahlten hell in der Dunkelheit.
The car's headlights shone brightly in the darkness.
When a person 'strahlt' (beams), the reason for the joy is often expressed with the preposition 'vor' (+ dative). Another common phrase is 'über das ganze Gesicht strahlen' (to beam from ear to ear).
Er strahlte vor Stolz, als seine Tochter das Diplom erhielt.
He beamed with pride when his daughter received the diploma.
The meaning 'to emit radioactive radiation' is used almost exclusively in a scientific or technical context. Signal words for this are 'radioaktiv' (radioactive), 'Reaktor' (reactor), or 'Uran' (uranium).
Das Messgerät zeigte an, dass das Material schwach strahlt.
The measuring device indicated that the material emits weak radiation.
to shine / seem
'scheinen' and 'strahlen' can both describe light. 'scheinen' is the normal word when light is simply there or falls on something, especially with the sun. 'strahlen' sounds stronger and more vivid: something gives off a lot of light or heat and appears very bright. They can be confused because both can be used with the sun and lamps. If you only want to say that the sun is in the sky, 'scheinen' is more natural. If you want to emphasize strong brightness, 'strahlen' fits better.

Nach dem Regen strahlte die Sonne wieder über den Dächern.
After the rain, the sun shone brightly over the rooftops again.
Heute scheint die Sonne, deshalb gehen wir nach draußen.
The sun is shining today, so we're going outside.