Don't be afraid of the difficult-looking words above! It's really quite simple: Homophones are words that sound the same, but have different meanings. Heterographs are homophones that also have different spellings. This can be quite confusing in spoken language, because the only way to tell homophones and heterographs apart is by the context in which they are used. The word "homophone" literally means "sounds the same," whereas the word "heterograph" means "written differently." In German, both nouns are neuter: das Homofon (or das Homophon) and das Heterofon (or das Heterophon).
Note too that in German, regional differences in pronunciation can sometimes make a set of words homophones in one region, but not in another. Let's take a look at some German heterographs today.
Monika aß sehr viel gekochtes Getreide.
Monika ate a lot of cooked grains.
Caption 4, Deutsch mit Eylin - Ernährungsformen
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Wenn die Nahrung knapp wird, begnügt er sich mit Aas.
When food becomes scarce, it makes do with carrion.
Caption 26, Die letzten Paradiese - Schätze der Natur: Südtirol
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It's ironic (and a bit disgusting) that the past tense of "to eat" (aß, from essen) sounds the same as the word for cadaver (das Aas). There's a certain logic, however, in the fact that most animal cadavers in the wild tend to get eaten by scavenger animals. When a homophone pair consists of a verb and a noun, you can construct funny-sounding sentences from them, such as: Er aß das Aas. By the way, only humans are referred to with the verb essen ("to eat"), whereas animals always take the verb fressen ("to devour"). And indeed, fressen also has a heterograph.
Das Pferd frisst gerne Äpfel.
The horse likes eating apples.
Caption 38, Deutsch mit Eylin - Pronomen
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Diese Frist kann verlängert werden,
This deadline can be extended
und zwar wieder nur durch einen einstimmigen Beschluss.
and only—indeed once again—through a unanimous ruling.
Caption 19, Brexit-Votum - Merkel warnt vor Spaltung Europas
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The third-person present tense of "to devour" (fressen) is frisst, and die Frist is a deadline or time limit. Der Pferd frisst Äpfel lieber ohne Frist. Nobody likes to be hurried to eat, right?
Er bot den Frauen ein Abkommen an.
He offered the women a deal.
Caption 55, Märchen - Sagenhaft - Die Weiber von Weinsberg
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Oje, das Boot von Opa Wutz hat kein Benzin mehr.
Uh oh, Grandpa Wutz's boat is out of gas.
Caption 16, Peppa Wutz - Sport
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Thus the past tense of "to offer" (bot, from bieten) is a heterograph of das Boot. Using both words in the same sentence, you can say something like: Das Boot bot uns viele Reisemöglichkeiten.
Wenn diese Temperatur so anhält,
If this temperature continues,
frieren die ganzen Seen in der Umgebung, wie ihr auch hinter mir sehen könnt, komplett zu.
all the lakes in the area will completely freeze over, as you can see behind me.
Captions 6-7, Unterwegs mit Cettina - Schlittschuhlaufen
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In this case, the plural of "lake" (der See) is Seen, and the verb "to see" is sehen. In the above example, both words of this heterograph pair are already in a single sentence.
Further Learning
Take a look at these examples of German homophones on Wikipedia and find some examples of the words used in a real-world context on Yabla German. Then see if you can create some German sentences using both homophones in the same sentence. You are allowed to make silly sentences, of course!