Resident but not ordinarily Resident - income earned in India or income arising out of business controlled from India taxable.
Non-resident - only income earned in India taxable.
INCOMES TOTALLY EXEMPT FOR NON-RESIDENT
1.Interest on notified securities or bonds and premium on re-demption of such securities. (S.10(4)(i)).
2.Interest on NRE/FCNR Accounts. (S.10(4)(ii)).
3.Interest on notified saving certificates subscribed in foreign currency by an Indian citizen/person of Indian origin. (S.10(4B)).
4.Income from units of UTI acquired in foreign exchange by Indian citizen/person of Indian origin. (S. 32(I)(aa) of UTI Act)
5.Interest on NRNR Deposits and other securities, bonds, sav-ings certificates notified S.10(15)(i)
6.Interest from notified bonds (7 year dollar bonds issued by the S.B.I. notified) purchased in foreign exchange, exemption continues even after person becomes resident. 
7.Interest paid by scheduled banks on RBI approved foreign currency deposits, to a NR or NOR (S. 10(15)(ivfa)).
SPECIAL PROVISIONS FOR NRIS - CHAPTER XIIA
S. 115C
a.NRI means an Individual, being a citizen of India or a person of Indian origin, who is 'not a resident'.
b.Investment income : income derived from a foreign exchange asset.
c.Foreign Exchange Assets: specified asset acquired by NRI out of convertible foreign exchange.
d.Specified assets are:
i.Shares of an Indian company.
ii.Debentures of or deposits with an Indian company, not being a private company.
iii.Any security of the Central Government.
iv.Other notified assets (no such asset has yet been notified).
S.115F : Exemptions for long-term capital gains:
Capital gains arising on transfer of a specified asset, is exempt from levy of any tax on fulfillment of the following conditions:
a.The asset transferred must be a long-term capital asset.
b.Net consideration must invested in certain specified assets
c.Investment to be made within 6 months of transfer.
d.If only a portion of the net consideration is reinvested, then proportionate exemption is allowed.
e.New asset must be held for at least three years.
S.115G : Option not to file income tax return:
NRI need not furnish a return of his income, if :-
a.his total income consists only of investment income or incomes by way of long-term capital gains or both, and
b.TDS has been deducted from such income.
S.115H : Continuance after NRI becomes resident:
Chapter-XIIA shall continue to apply to such income even after an NRI becomes a resident, if he furnishes a declaration along with the Return of Income to that effect. Tax would then be levied at 20% until transfer/conversion into money of such assets.
S.115I : NRI may opt out:
An NRI may elect not to be governed by the provisions of Chapter XIIA for any A.Y. by furnishing a written declaration to the A.O. with his return of income. His total income for that
A.Y. shall be computed and tax on such total income shall be charged in accordance with the other provisions of the Act.
SPECIAL CONCESSION FOR CAPITAL GAINS(SPECIFIED ASSETS)
Expl. to S.48(1)(a) : Convert original cost, expenditure on trans-fer and sale consideration into foreign currency in which investment was made (at prescribed rates) and reconvert capital gains into rupees again. The benefit of indexation will not be available to the NRI.