TEA vs COFFEE –Bitterness-

In taste-wise, tea has something in common with coffee. Both have "bitterness", don't they?. Look like the same, but don’t you think they have different bitterness respectively? 

It is not easy to explain the taste, but in Japanese we use different words for them, which are "shibui" for bitter taste of tea while "nigai" for that of coffee. It is completely my opinion, but I feel that tannin-ish taste could be "shibui", caffeine-ish taste is "nigai". 

In English, you may say "astringency “, "pungency “ or whatever other than "bitterness". How would you describe the bitterness of tea? How would you distinguish tea-ish bitterness from coffee-ish bitterness? I am very curious......:-)