heulen
to cry
To cry loudly and with tears, often in an uncontrolled or childlike way.
Das kleine Kind begann zu heulen, als es sein Spielzeug verlor.
The little child began to cry when it lost its toy.

to cry / howl
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to cry
To cry loudly and with tears, often in an uncontrolled or childlike way.
Das kleine Kind begann zu heulen, als es sein Spielzeug verlor.
The little child began to cry when it lost its toy.

The subject of the sentence reveals the meaning: if a person 'heult' (cries), they are crying. If an animal, e.g. a wolf, 'heult' (howls), it makes a long sound. If an object, e.g. a siren, 'heult' (howls), it produces a loud sound.
Er heulte vor Glück, als er die Nachricht hörte.
He cried with joy when he heard the news.
When it refers to people, 'heulen' (to cry) is a very colloquial and emotional word for 'weinen' (to cry). It describes loud, often uncontrolled crying.
Hör auf zu heulen, es ist doch nichts Schlimmes passiert!
Stop crying—nothing terrible happened!
A fixed and very vivid expression is 'Rotz und Wasser heulen'. It means that someone is crying extremely hard and without restraint.
Nach der traurigen Nachricht hat sie Rotz und Wasser geheult.
After the sad news, she cried her eyes out.
to laugh
'lachen' and 'heulen' both describe a strong expression of emotion. 'lachen' fits joy, fun, or amusement. 'heulen' means to cry loudly and with tears, and is more associated with pain, fear, or great sadness. So the contrast is not only in the facial expression, but above all in the feeling: someone who laughs usually shows something positive; someone who 'heult' usually shows a strong negative emotion.

Das Kind heulte laut, weil es sein Spielzeug verloren hatte.
The child cried loudly because it had lost its toy.
Nach dem lustigen Film mussten alle im Wohnzimmer lachen.
After the funny movie, everyone in the living room had to laugh.