Does the CG tax differ as per period of holding an asset?

Yes, tax on Capital Gain is different for Short Term Capital Gain (STCG) and Long Term Capital Gain (LTCG).

Tax on Long Term Capital Gain:

If assets are held for more than 36 months prior to sale then they are called long-term assets and their transfer results in long-term capital gain which is taxed at the rate of 20%.

There is an exception to this rule:

In case of securities (where Securities Transaction Tax (STT) is paid on sale) period for considering Long Term Asset is 12 months only and said Long Term Capital Gain is exempt. In case STT is not paid on sale of securities, then Capital Gain is taxable @ 20% with Indexation benefit or 10% without Indexation benefit. Taxpayer can choose beneficial option.

Short Term Capital Gain:

Any transfer of assets held for lesser than these periods would result in short-term capital gain. This is taxed at normal rates in respect of all assets except securities (where STT is paid on sale). In case of securities (where STT is paid on sale) the rate of tax is 15%.