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A true biopsy is a medical procedure in which the cat is anesthetized and a sample is taken surgically.
A needle aspiration is where they use a needle to draw back some cells and then analyze this under a microscope.
If you want to know what you're dealing with and seek treatment, you need to go for the biopsy. If you feel like she has lived a good life and you don't want to persue further treatment, you are not required to get the biopsy.
At this age, treatment might just consist of keeping your cat comfortable until his last days. You never know.
I am very sorry that you are going through this.
Let me know if you have more specific questions. I would be happy to answer them.