Hydra reproduces by regeneration or budding while amoeba reproduces using binary fission .
When one mature unicellular organisms like amoeba splits into two daughter individual the process is called binary fission.
in amoeba the nucleus divides into two nuclei .then the cytoplasm divides into two parts each containing a nucleus .a constriction develops in the body which gradually deepens to form two daughter individual

in budding as seen in hydra a small outgrowth appears on the body of organisms. this outgrowth is called bud. the bud grows and finally gets detached from the parent body and begins to live as an individual and independent.
since new individual develops from the bud in hydra this type of reproduction is called budding.

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