I can only remember times I’ve heard “Better safe than sorry” used to encourage taking an action that had a high chance of being a small waste of time or effort, with a small chance of minimizing the consequences of an unlikely event that would make it worth it, such as taking an umbrella in case it rains or seeing a doctor in case there is something wrong. I can similarly only remember “Nothing ventured, nothing gained” used as a way to encourage taking actions specifically usually also ones that have a low chance of a high reward, and a high chance of a small loss. These do not seem like opposites to me.
I can only remember times I’ve heard “Better safe than sorry” used to encourage taking an action that had a high chance of being a small waste of time or effort, with a small chance of minimizing the consequences of an unlikely event that would make it worth it, such as taking an umbrella in case it rains or seeing a doctor in case there is something wrong. I can similarly only remember “Nothing ventured, nothing gained” used as a way to encourage taking actions specifically usually also ones that have a low chance of a high reward, and a high chance of a small loss. These do not seem like opposites to me.