Are coriander and cardamom the same thing?

No. Cumin (the spice) is the dried seeds of the plant Cuminum cymenum.

Cilantro refers to the leaves of the plant Coriandrum sativum. The spice coriander is the dried fruits ("seeds") of the same plant, and tastes different (among other things, it doesn't have the "dish soap" taste that some people perceive in the leaves; the ability to detect this appears to be genetic).

The two plants are in the same "family", but that's not saying much ... so are dill, anise, and carrots.