There is really no pronounced difference between safe and secure. But it is interesting to note their etymologies.
Safe: OFr sauf, Latin salvus
Secure: Latin sēcūrus, from sē -without and cūra - care
It is clear that secure had a different root, originally meaning "without care". Today these words overlap very much and the distinction is hardly perceived in daily usage.
That said, I would go with @JLG's answers for the usage in your sentences. Secure is commonly used with documents (it's financial security and not financial safety, for example). As such secure is slightly more powerful than safety when it comes to describing the extent of protection.
- The birds' nests are high up, safe from predators.
- These elephants are relatively secure from poachers.
- Make sure you keep these documents secure.
- Keep your credit cards in a secure place.
- I always feel safe when I'm around my big dog.