About similarities of sayings in different languages

While doing an idiomatic Spanish exercise to learn some of the language structures better, I couldn't help but notice a very curious detail that never came to my mind: some of the most famous sayings that people across different cultures use regularly, repeat themselves in the structure even in different languages. One of the most difficult things in a language is to learn the idiomatic expressions; whole books on this topic exist for a reason, because every language has its own way to say, for example, that something is very expensive or someone does not know his job very well. Nevertheless, the parallels between Spanish and Russian in the sphere of sayings genuinely surprised me. Some examples of that:

1. "A caballo regalado no le mires el dentado" VS "Дареному коню в зубы не смотрят".
Both of them signify that you must accept any gifts with gratitude and without criticizing them, but the fact that both structures are absolutely identical is really astonishing. Language contact definitely took part in this, as it's impossible to think that both absolutely different languages came up with the same metaphor of such an expression. Additionally to it, most of the modern phrases are so called "calques", literal translations adopted from different cultures or dominant languages.
2. "Más vale pájara en mano que ciento volando" VS "Лучше синица в руках, чем журавль в небе".
Meaning is that it is better to have small yet secure advantage than to risk losing it to something larger. I did some research on the origins of this saying in Spanish, and apparently it came from Latin. The Russian version of it came from an Ancient Greek Aesop's tale. It is very interesting that even while having different origins, both sayings use the metaphor of bird as something unreachable. The Spanish one compares the quantity of the birds (one in the hands or one hundred flying), while the Russian one creates the same contrasting effect with the very size of birds (a sparrow in the hand or a crane in the sky). These small details really portray the complexity of the language transfer mechanisms.

I think that after a more profound research I could come up with even more examples of such unexpected linguistic parallels. Even though most of them can probably be explained with a lot of language factors, I find it absolutely fascinating how languages exist as living entities instead of a dry set of fixed rules.