BCA is an acronym for Bachelor of Computer Application. It is an undergraduate course in the University. The total period for this course is just three years which translates to six semesters. The program is meant for people who feel the need to breach the gap between the study of computer and it's application. If you desire to know more about computer and it's applications, the course is for you.
Bachelor of Computer Applications course consists of core courses in programming with, algorithm and data structures, advanced programming with C, computer organization and network fundamentals while MCA means Master of Computer Application. This course is a post-graduate course. It's for those who desires to learn more about about computer and it's application. The two courses focus mainly on core and basics of computer science.
BCA and MCA may have different meanings depending on the place where you live. The most common meaning for BCA is Bachelor of Computer Applications. This is a course that people take when they want to show their proficiency in using computers. Unlike Computer Science which is usually a 4-year course, BCA is only 3 years.
MCA is known to be Music Corporation of America. Based on its name, you can already guess that this is related to music. It used to be a very popular company but there are so many things that have occurred that made the company lose its customers. It is obvious that these two abbreviations are different from each other.
The first you mention, BCA, stands for the Bureau of Criminal Apprehension. The second stands for the Motor Club of America and also for the Museum of Contemporary Art.
Either way, there's a world of difference between the first and the second! It also depends on which country you are in.