You are right, there are various roles which are available in analytics domain. Let me try and summarize some of them:
Designations used in the industry:
Statistician - A person who specializes in statistics and acts as an expert to a team of business analysts. He is typically the go to person for complicated test designs, advisory on better statistical / predictive modeling. Statisticians are typically people with at least a Masters degree in stats.
Solution architect / Big Data Architect - Responsible for the design of data architecture. This person would be responsible for designing and maintaining the infrastructure so that various data scientists and business analysts can do their work efficiently. This person would typically be responsible for deciding the RAM on the server, which server to deploy, which database to use, how to design Hadoop clusters etc.
Data Analyst - Data Analyst is typically referred to as a person who is responsible to cleaning and maintaining data. The person will be responsible to make sure that all the data flowing in various statistical models and dashboards is clean, free of data entry errors and is transformed as per the business requirement.
Consultant - Typically referred to the person, who will liaison with the clients on various analytics solutions which can be used for their business solutions. The role of consultant would be to take amorphous problems from the clients and then put an analytics framework around it.
Business Analyst - This designation is one of the most loosely used designation in the industry. Business Analyst can be used to refer to person playing the role of a consultant or data analyst or even statistician in many places. Traditionally, business analyst referred to a person acting as a mediator between business and statisticians / technicians.
Data Scientist - Data scientist is a relatively new term, which refers to people who know stats, programming and posses business knowledge as well. Here is a nice definition of a Data Scientist: > A data scientist is someone who is better at statistics than any software engineer and better at software engineering than any statistician.
As you can see, there is a lot of overlap in how these terms are used and hence for the remaining answer I will use Business Analysts for people who slice and dice data with various statistical tools to come up with data based strategies.
If the person is also required to scrape the data from web or design a software / product basis machine learning, I will refer to him as a data scientist.
Paths to become a data scientist:
There are several ways for you to enter data science world. You would be expected to come from a quant background like Maths / stats / economics / engineering. If you know programming, that is a plus.
If you come from a business role, you will need to pick up on quant and tech skills. If you come with tech skills, you will need to pickup business skills.
If you come from research background, and know programming skills with R and Matlab, you should be considered for the position of data scientist. So, you should pick up on domain specific knowledge
Hope this helps