Chernobyl was an outdated design known to be dangerous at the time it was made, and something like the Chernobyl incident can't happen on anything newer. A study found statistically insignificant rises in cancer rates from the 3 Mile incident.
I recommend the book Atomic Accidents, it's very informative and I believe it went over specifically why a nuclear plant can't just explode like an atom bomb or even really help you make one.
No, your average nuclear plant doesn't have the makings of an atom bomb. But countries that are running nuclear power plants have an obvious incentive to create enrichment facilities for their nuclear power. These facilities are similar to those that enrich further for a nuclear bomb. Several countries have achieved nuclear bombs this way.
Furthermore nuclear plants do not all work the same way. There are advocates of thorium nuclear plants, because thorium is a much more abundant fuel source that should be able to operate more cleanly than uranium. However those plants generate uranium-233 which can be potentially separated through chemical processes in plants that are a lot easier to hide than centrifuges used for enrichment.
Both ways, nuclear power can be a step on the way to nuclear proliferation.