Hüte means "hats" in the plural, in the nominative, genitive, or accusative case: ich kaufe Hüte "I buy hats"
Hüten means "(to) hats" in the plural dative case: mit den Hüten "with the hats"
hüte means "(I) take care of or herd": ich hüte Schafe "I herd sheep"
hüten means "(we, they) take care of or herd" or the infinitive "(to) take care of or herd".
Remember that nouns are capitalised in German!
How can you tell the difference between "wear" and "are wearing"?
Only from context (i.e. is this sentence about something that is happeningh now or something that happens regularly).
Without context, both translations can make sense and will be accepted.
Standard German does not make this distinction in its grammar.
In English, 'carrying hats' and 'wearing hats' can be two different things. How could you tell the difference in German if 'tragen' means both 'to carry' and 'to wear'?
Or you could specify sie trägt einen Hut in der Hand (she is carrying a hat in her hand) versus sie trägt einen Hut auf dem Kopf (she is wearing a hat on her head) / sie hat einen Hut auf (she has a hat on; she is wearing a hat).