Do Institutional and retail Algo traders have different Government Tax structures than who executes order manually?

Algo trading is basically to capture small movements in the market. If you look at the Nifty Index Future, considering the tax structure for Retail users, break even happens around 2 points. I believe Algo traders targets much smaller than this.

Can you help me understand how does it work for Algo traders?

Do Institutional and retail Algo traders have different Government Tax structures?

Taxation is exactly same for everyone in terms of STT, Stamp duty, service tax and all. If you are talking about income tax, institutions actually pay higher taxes than individual retail.

Not all algo trading is about capturing small moves in the market.