c difference between a B.Tech and Polytechnic engineering courses is that a B.Tech is a degree course while a Polytechnic is a diploma course in engineering.
One can opt for a polytechnic course just after 10th or it can also be done after 12th. But one cannot opt for B.Tech only after 12thwith physics, chemistry and maths as compulsory subjects. The duration of a polytechnic course is of minimum 3 years but you can take a lateral entry in polytechnic if you have done ITI for which the duration of the course will then be 2 years. The admissions are based on Polytechnic Entrance Exam which happens in the month of May or June, in some states polytechnics also take direct admission in 3 years diploma course. Many  government companies might recruit you for techincal jobs