This is the dictionary defenition for distinguish:
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dis·tin·guish (d-stnggwsh)
v. dis·tin·guished, dis·tin·guish· ing, dis·tin·guish· es
v.tr.
1. To perceive as being different or distinct.
2. To perceive distinctly; discern: distinguished the masts of ships on the horizon.
3. To make noticeable or different; set apart.
4. To cause (oneself) to be eminent or recognized: They have distinguished themselves as dedicated social workers.
v.intr.
To perceive or indicate differences; discriminate: distinguish between right and wrong.
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http://www.thefreedictionary.com/distinguishable
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The rest of the words you have given are derived from the word 'Distinguish'. You can easily make out their meaning on your own from the description given above.
