It appears that they both describe the upper boundary mass that a cloud in space may inhibit before gravitational collapse. From Wikipedia, on Jeans mass/Jeans instability:
"...Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium [...] The Jeans instability likely determines when star formation occurs in molecular clouds."
Wikipedia on Bonnor-Ebert:
"...the Bonnor–Ebert mass is the largest mass that an isothermal gas sphere embedded in a pressurized medium can have while still remaining in hydrostatic equilibrium. Clouds of gas with masses greater than the Bonnor–Ebert mass must inevitably undergo gravitational collapse to form much smaller and denser objects. As the gravitational collapse of an interstellar gas cloud is the first stage in the formation of a protostar, the Bonnor–Ebert mass is an important quantity in the study of star formation."
The phrasing varies but I feel that, unless I've misunderstood, they're surely referring to the same phenomenon? That after a certain mass is reached, the gas cloud/sphere is not in hydrostatic equilibrium, therefore it collapses due to gravity acting inwards overcomes the gas' pressure acting outwards (in simplified terms), and that this in turn is seen in the study of star formation. What is the difference between the two, and when is one more appropriate to study than the other? Planet formation vs star formation? Is it to do with the medium (BE mass mentions pressurised medium and J mass does not)?
I suspect that the answer is glaringly obvious but Google is only turning out notes or papers on one or the other, but no one comparing the two (as far as I've been able to find).