Chastise means to punish or castigate. Chasten means to discipline or subdue. So chastisement is harsher, and chastening can be subtle and event gentle. Both verbs are rooted in the adjective chaste, and they were interchangeable until a century or two ago. They are still often mixed up, but careful writers keep them separate.
Examples
Chasten, the less common of the two, means to discipline or to subdue—for example:
With no kind of critical tradition to chasten him, his force is often misguided and his work shapeless … [The Danish History]
She seems more committed to small, common-sense government than any of them and could potentially rally the public to chasten a spendthrift Congress. [Toronto Sun]
And in reading these examples, note how those who are chastised are punished or harshly criticized rather than merely tamed or brought under control:
Many critiques of Badu chastise her for being nude around children. [Alternet]
He went on to chastise the use of RNC funds at a Los Angeles strip club and called it “the straw that broke the camel’s back.” [Seacoast Online]
The kneejerk response to this is to chastise the “Spanish system” as profoundly unequal and top-heavy. [Times Online]
