Tax deduction vs exemption:

 In deduction, the amount is first added to the taxpayer's income and then in accordance with the rules, deduction is allowed. For instance deduction per se section 80C, 80D, 80G etc.
While, in exemption, some particular income stream do not attracts tax liability. Such as is in the current case allowances for medical and travel were exempt from tax. But have now been proposed to attract liability with effect from Fin year 2018-19.

Exemptions allowed from particular income stream only while deductions deducted from gross total income:

Before arriving at the gross total income, some of the provisions that allow for tax exemption are accounted for by deducting the relevant amount in partial or full from the allowed income head and then the arrived at income streams are added to reach the gross total income.

Tax deductions allowed to promoted savings and investments:

 Another purpose with which tax deductions came into place is to promote savings and investments by a taxpayer. As for eg: Section 80C allows deductions to the tune of Rs. 1.5 lakh from the gross total income for investments in various small saving schemes, insurance and other expenses.
On the other hand, the tax exemption provision boosts the section for which the exemption is allowed.

Section 80C to 80U covers deductions while Section 10 includes exemptions:

 All of the deductions are the part of the above mentioned sections. Also to be noted is that the income that allows exemption is tax exempt while that allows deduction reduces tax outgo by allowing deduction.
Tax deductions is condition based and not available to all taxpayers while tax exemption is available to all

Example to understand tax deduction and tax exemption:

 Tax deduction say allowed in Section 80C decrease your gross total income by the amount of investments or expenses made in a particular financial year. While exemption such as that leave travel allowance etc are allowed to be reduced from salary income.