der Krebs
cancer
A serious disease in which body cells multiply uncontrollably and destroy healthy tissue.
Die Forschung macht große Fortschritte bei der Behandlung von Krebs.
Research is making great progress in the treatment of cancer.

cancer / crab
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cancer
A serious disease in which body cells multiply uncontrollably and destroy healthy tissue.
Die Forschung macht große Fortschritte bei der Behandlung von Krebs.
Research is making great progress in the treatment of cancer.

Since 'Krebs' has several meanings, context is crucial. In a medical context (doctor, hospital), it refers to the disease. In nature, by the sea, or in a restaurant, it refers to the animal. In conversations about birthdays and horoscopes, it refers to the zodiac sign.
Die Ärzte konnten den Krebs erfolgreich behandeln.
The doctors were able to treat the cancer successfully.
In connection with the disease, the preposition 'an' is often used, for example in 'an Krebs erkranken' (to develop cancer) or 'an Krebs sterben' (to die of cancer). You can also say that someone 'Krebs hat' (has cancer).
Leider ist er schon jung an Krebs erkrankt.
Unfortunately, he developed cancer at a young age.
When talking about the animals, the plural form 'die Krebse' (the crabs/crayfish) is often used, especially when it is about catching or eating them.
In diesem Restaurant kann man frische Krebse essen.
You can eat fresh crayfish in this restaurant.
When it is about the zodiac sign, 'Krebs' (Cancer) is often used in the fixed expression 'vom Sternzeichen Krebs sein' (to be Cancer by zodiac sign) or as an answer to the question about someone's zodiac sign.
„Was ist dein Sternzeichen?“ – „Ich bin Krebs.“
'What is your zodiac sign?' — 'I'm Cancer.'
tumor
'Krebs' and 'Tumor' both belong to the medical field and have to do with uncontrolled cell growth. 'Krebs' means a serious malignant disease. A 'Tumor' is a growth of tissue in the body. It can be malignant, but it does not have to be; there are also benign tumors. For this reason, the words are not always interchangeable. Learners may confuse them because people often also talk about a tumor when discussing cancer. The important point is: a malignant tumor can be cancer, but not every tumor is cancer.

Bei ihrem Vater wurde vor zwei Jahren Krebs festgestellt.
Her father was diagnosed with cancer two years ago.
Der Arzt sagt, dass der Tumor gutartig ist.
The doctor says that the tumor is benign.