Yes, they are similar, but that's because they're both derived from the definition of stable equilibrium. Stable equilibrium is a state of a system in which it has minimum energy. Hence, from the definition of energy, any deviation from a stable equilibrium would create a force that would drive the system back to equilibrium.
Something interesting is that they were living in about (loosely) the same time period. Wonder what would have happened if scientists didn't read or became interested in each others work. I wouldn't want it any other way that it is today. Thanks for that!