No, single entry Schengen Visa will give you one single entry for whole Schengen Area, for the days mentioned on visa sticker. You may freely move around Schengen provided you are within the dates, days & purpose allowed on this visa. Keep in mind that few EU countries are not Schengen members, like Croatia; few Schengen members are not EU members, like (Switzerland), few countries geographically situated in Europe are neither in EU nor in Schengen, like Andorra, thanks to Henning) So, you can/may stay/roam in whole exact Schengen area only.
Borders between Austria and Hungary might be closed because of "migrant" situation, but all they check is if you have required visa/documents. So landing in Budapest, then going to Vienna, and coming back to Budapest will not be counted as any exit from Schengen Area. Hungary and Austria are still members of Schengen, and are still honouring these visas.
As you are Indian, (I am also), think Schengen Area and members as India and its states (only for C Type visa). There maybe a strict border-checking at certain state borders, and at few other border crossings, there maybe just a change in road surface.
Also, the Paper Visa Form has not much space to write multiple countries in destination field. So, the formula of choosing destination (& thus embassy) is:
- in which member state you will spend most of your planned days, no matter you entered or exited anywhere else? This willbe your destination.
- if you will spend same number of days in two or more member states, then the first member state will be your destination for visa form purpose.
As few embassies use online form for visa application, they give you choice of selecting only one member state as destination.
Point of entry or member state of entry will be your first landing airport in schengen area, no matter how short is the transit. In first few applications I did not know this, and thought I will stay air side in my schengen transits, and will "enter" into schengen only at last final destination airport, but was wrong. As soon as you touch down in Schengen, you are in from that airport/country. For KLM fligjts, its AMS/Netherlands most of the time.
Excerpt from France Embassy in USA, on whether one should apply to them for Tourist Schengen Visa (of course if applicant is applying from USA)
You have to apply with a French Consulate, if :
You wish to go only to France ;
You wish to travel to several Schengen States, but France is the country where you are going to spend most of the time of your trip ;
You wish to travel to several Schengen States, with no main destination (the duration of your stay is strictly equal in each country), but France is your first point of entry.