When examining the relative advantages of chrome and stainless steel as bearing materials, it's not just about corrosion resistance.
Chrome steel (high carbon chromium steel) is the most commonly used steel for bearings. It is harder than stainless steel so gives longer life ratings.
However it does not perform as well at higher temperatures.
Above 120C it undergoes greater dimensional changes and load capacity reduces.
Intermittent temperatures up to 150C can be tolerated, but a constant 150C or even higher would reduce bearing life.
Heat treatment will allow the bearing to cope with roughly 170C constant.
The most common grade of stainless steel for bearings is 440.
It is hardenable and tough enough to take heavy loads (about 20% less than chrome steel) but is corrosion resistant and should cope with constant temperatures of up to 250C constant and 300C intermittent.
It is often wrongly assumed that all stainless steel is nonmagnetic.
440 stainless certainly is magnetic.
It is also not completely corrosion resistant and is affected by salt water and many acids/alkalis.
316 grade is far more corrosion resistant (hence the nickname 'marine grade') and nonmagnetic but much softer and can only cope with small loads and speeds.
As it is not hardenable, it cannot easily be ground so 316 bearings are semi-precision with a rougher feel.
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