
herzhaft
savory / hearty
Refers to foods that taste strong, spicy, and not sweet. Often used for substantial, hearty meals.
Nach der Wanderung gab es eine herzhafte Gulaschsuppe.
After the hike, there was a hearty goulash soup.
hearty / savory
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savory / hearty
Refers to foods that taste strong, spicy, and not sweet. Often used for substantial, hearty meals.
Nach der Wanderung gab es eine herzhafte Gulaschsuppe.
After the hike, there was a hearty goulash soup.

heartily
Describes an action that is carried out forcefully, full of energy, and without hesitation.
Als er den Witz hörte, musste er herzhaft lachen.
When he heard the joke, he had to laugh heartily.
The word is made up of 'Herz' (heart) and the suffix '-haft' (-like, having the quality of). So it literally means something like 'heart-like' or 'full of heart' and describes something strong, substantial, or full of feeling.
Nach der Gartenarbeit schmeckt ein herzhaftes Abendessen besonders gut.
After gardening, a hearty dinner tastes especially good.
You can easily recognize the meaning of 'herzhaft' (hearty/savory) from the context. In connection with food and drink, it means 'deftig' (hearty/substantial) or 'würzig' (spicy/savory). In connection with actions like laughing or yawning, it describes them as strong and uninhibited.
Zum Frühstück isst er am liebsten etwas Herzhaftes, wie Wurst und Käse.
For breakfast, he prefers something savory, like sausage and cheese.
When it comes to food, 'herzhaft' (hearty/savory) is often used for certain meals. Typical combinations are: 'ein herzhaftes Frühstück' (a hearty breakfast), 'ein herzhafter Eintopf' (a hearty stew), or 'eine herzhafte Brotzeit' (a hearty snack/light meal).
In der Berghütte wurde uns ein herzhafter Eintopf serviert.
In the mountain hut, we were served a hearty stew.
In this meaning, 'herzhaft' (heartily) is usually used as an adverb to describe a verb more closely. It then stands directly with the verb and expresses the intensity of the action.
Die Kinder spielten und tobten herzhaft im Garten.
The children played and romped heartily in the garden.
warm / heartfelt
Herzlich and herzhaft can both describe genuine, uninhibited laughter. Herzlich highlights warm and friendly joy, while herzhaft emphasizes strength and exuberance. Herzlich suits a warm moment shared with others, whereas herzhaft is more appropriate for loud, hearty laughter.

Nach der überraschenden Pointe lachte sie herzhaft und laut.
After the surprising punchline, she laughed heartily and loudly.
Beim Wiedersehen lachte sie herzlich über seine vertraute Geschichte.
When they saw each other again, she laughed warmly at his familiar story.