VAT is a type of consumption tax that the buyer pays for the value that is added by the seller from when it is bought to when it is sold. It is paid at every exchange meaning nay purchase or sale. It can be levied at multiple stages from production till consumption, with each stage adding some value to the good. It is calculated only on the extra addition of value and not on the entire product. This is a kind of indirect tax meaning government is not asking the individual to pay tax but when they buy any product or service, a part of that cost is going to the government.
GST is the new single comprehensive destination based tax system that is introduced newly in the country and has since then revolutionized the Indian taxation system. With many number of taxes that were levied by both central and state tax calculation remained as a nightmare and with the introduction of GST the whole hassle has been simplified. It has unified number of taxes that were existent in the country since long. It is a destination based tax system meaning that we end user is the one who is going to pay the tax. The rates have changed since GST is launched and the confusions around GST has not yet subsided. GST is shared by both state and central governments.
Professional tax is the tax that is paid by any professional which includes lawyers, doctors, charted accountants etc. or any one who is earning through a regular income. It is a tax that is levied by the state and each state has different rates and different procedures of collecting the tax. This is a kind of direct tax where the government is directly collecting it form the individuals.