NEET is the national entrance for medical courses where as IIT JEE is the entrance examination for varied courses in engineering at IIT's and NIT's (for IIT JEE you have to qualify JEE MAINS).

For NEET you have to give three papers namely Physics, Chemistry and Biology. The exam is of MCQ type and is one of the tough exams in India. To be eligible for NEET you need to score at least 50% marks in 10+2 (additional 5% less for the reserved candidates). Through NEET you may get admissions to popular medical courses like MBBS, BDS, BHMS, BAMS etc as well as some paramedical courses.

To know more about NEET you may visit the link provided below:

https://medicine.careers360.com/exams/neet

Now for IIT JEE you have to qualify JEE MAINS exam which is less tougher than IIT JEE but is tough to qualify as it has some tough and challenging scenarios in time management. For IIT JEE or JEE MAINS you have to give a CBT examination for the papers Physics, Chemistry and Mathematics. On qualifying the cutoff of JEE MAINS you will be eligible to give IIT JEE. For admission through counselling in IIT/NIT or through JEE MAINS you need to score at least 75% marks (Although these barrier is removed).

Some of the popular IITs are: IIT Bombay, IIT Delhi, IIT Kharagpur, IIT Madras, IIT kanpur, IIT Guwahati.

I hope my answer helps. All the very best for your future  endeavors!