What are the main differences between Functional And Technical Consulting?

I have been in the industry for approximately 25 years, currently providing various forms of IT related consulting services to the New York metro area, and have "never" heard anyone use those categorizations when hiring consultants.

I can venture an educated guess and say that "Functional Consulting" is what many companies call "Business Analysis" or "Business Architecture", which specifically have to do with things like understanding and providing solutions for processes, data, roles and responsibilities, etc. Given that description, I'd venture an educated guess and say that "Technical Consulting" represents someone who can come in and understand and provide technical solutions, such as a "Technical Analyst" or "Technology Architect".

There are roles that bridge both "functional" and "technical" areas. Such roles are often referred to as an "Enterprise Architect", who is typically focused on strategic solutions for enterprises, or "Solutions Architect", who typically focuses on narrower, more specific problems to solve. Such Architects are usually responsible for understanding and providing solutions for, both, functional and technical issues or problems.

Given that the above attempts to answer your Question #1, here are some answers for your other questions...
 

How did you get into this role either of them?

My career evolved, over time, into such a role. After many years of working for other people, I wanted to start my own businesses. Consulting seemed like the logical choice.
 

How a newcomer can break into this kind of roles and what is required of him/her in terms of skills, qulifications, knowledge, experience etc?

It often takes many years of practice to be good at anything you choose to do and to build up a reputation that allows customers to trust that you can assist them with their problems. It comes down to:

1) Your technical skills, 
2) your business skills and 
3) your people skills.
 

Can a person from a non-programming background become either funcational or technical consultant? What is the best path for him functional one or technical one?

Non-technical people become Business Analysts (what you call "functional consultant") all the time. However, how much you know or how good you are dictates how much companies are willing to pay you for your services. Many years of experience and established relationships and references usually help with this.

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