Question: It seems as if both words mean *to humiliate and degrade*?

Answer: 
To *abase* is to behave in a way so as to belittle or degrade someone.

To *abash* is to cause someone to feel embarrassed or ashamed.
I wonder if you're conflating or confusing words here…

* abase - behave in a way so as to belittle or degrade
* abash - embarrassed, disconcerted, or ashamed
* bash - (3) criticize severely
* debase - reduce (something) in quality or value; degrade

From the note on **humble** in the *New Oxford American Dictionary*:

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> *Humble* and *humiliate* sound similar, but *humiliate* emphasizes shame and the loss of self-respect and usually takes place in public (: *humiliated by her tearful outburst*), while *humble* is a milder term implying a lowering of one's pride or rank (: *to humble the arrogant professor by pointing out his mistake*).
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> ***Abase*** suggests groveling or a sense of inferiority and is usually used reflexively (: *got down on his knees and abased himself before the king*), while *demean* is more likely to imply a loss of dignity or social standing (: *refused to demean herself by marrying a common laborer*).
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> When used to describe things, *debase* means a deterioration in the quality or value of something (: *a currency debased by the country's political turmoil*), but in reference to people it connotes a weakening of moral standards or character (: *debased himself by accepting bribes*).
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> *Degrade* is even stronger, suggesting the destruction of a person's character through degenerate or shameful behavior (: *degraded by long association with criminals*).
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