
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.

beam
To have a glowing face because of joy, happiness, or pride; to look very happy.
Nachdem sie die Prüfung bestanden hatte, strahlte sie über das ganze Gesicht.
After she had passed the exam, she was beaming from ear to ear.

radiate
To have a strong positive effect or aura on the surroundings.
Ihre innere Ruhe strahlt auf alle um sie herum aus.
Her inner calm radiates to everyone around her.

emit radiation
To emit radioactive or electromagnetic radiation.
Der beschädigte Reaktorblock strahlt immer noch stark.
The damaged reactor block is still emitting strong radiation.
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
When referring to the sun, both words can describe visible light. “Scheinen” tends to emphasize that the sun is visible or illuminates a place, while “strahlen” emphasizes the strong effect of the light radiating outward. “Strahlen” is therefore often a good choice for especially bright light.

Die Sonne strahlt heute kräftig auf den Garten.
The sun is shining brightly onto the garden today.
Die Sonne scheint heute durch die Wolken auf den Garten.
The sun is shining through the clouds onto the garden today.