Hi Kushagra! B. Arch and M. Des both are different course from each other. 

WHAT IS B. ARCH? 

B. Arch or you can say bachelor in architecture course which is an under graduation course. The duration of this course is 5 years. Various colleges that offer architecture course, take admission through various entrance exams. Such entrance exams for architecture are- NATA, JEE Mains paper 2, HITSEEE,  AAT.

SUCH EXAMS HAS DIFFERENT ELIGIBILITY CRITERIA. SUCH AS--

• NATA- National Aptitude Test In Architecture is a national level entrance exam conducted by council of architecture for admission to 5 years B. arch degree course at various institutions in India. There is no age eligibility criteria for NATA mentioned by CoA in particular. But the candidates who are willing to give NATA must have completed their 10+2 examination or 10+3 degree from any recognized board with mandatory subjects such as physics, chemistry and mathematics. 

• JEE- MAIN paper2- Joint Entrance Exam – Main is an national level all India exam conducted by  NTA to take admission of the candidates who are willing to pursue architecture as well as various courses of engineering. There are also no age limit to sit for JEE- MAIN. Candidates must complete their 10+2 examination with mandatory subjects mathematics, physics and chemistry from any recognized board. 

WHAT IS B. DES? 

B. Des or bachelor’s of design in a under graduation course for design. The duration of this course is 4 years which includes total 8 semesters. This field has many specifications such as B. Des in fashion design, interior design, products design, textile design, accessory design, game design, communication design, graphic design and so on. The candidates for B. Des can join this course right after completing their 12th exam, but to get chance in the best designing college, they have to sit for entrance exams and to crack those exams, candidates need basic skills in design, because those exams are based on design aptitude tests and tests candidate's drawing and Idea skills.

ELIGIBILITY FOR B. DES

• Candidates must have 10+2 or 12th degree in any relevant stream from any recognised board. 
• Candidates can also have 10+3 degree in any relevant stream. 
• Candidates have to go through entrance exams of their preferred college and score at least 50% aggregate marks. 
• The age limit to study B. Des course is minimum 19 or 20 years according to the preferred institutions.

Hope this will help you!