is there big difference between data Science , big Data and database?
Well, they are absolutely different things but that are somehow linked. I gonna go through each of them.

Data Base

Think of a data base (DB from now) like a computer which only purpose is to store data accesable to be read. By data, and focusing only in SQL-like DB, I mean basically tables of information like and excel file with columns and rows. You can think of a SQL DB like an ecosystem of excel tables which share some common field. So basically a DB is a hardware infrastructure which allows to write and read a given amount of information within it (in the very beggining they were plain computers, of course with the rise of internet specialized hardware appeared). You can build your own DB in your personal computer.

Big Data

" An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed ... for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes." P.S.Laplace

Laplace did not think over it very deeply before formulate his sentence, obviusly if god had come to him and give what he wanted soon or later he would have realized all that information was indeed useless for him. Where could him store all that? From where should him start to read? What can he do with such amount of information he could never end to compute? In case he could read everything what should he calculate first?

These all are questions Big Data tries to answer and find a solution to. Big data appeared together with the huge websites internet gave birth, such as Amazon or Google. At some point they need to store so many information that it was imposible to store it in a single computer, not even in a big one, so they need to use a set of computers for which previous standard technologies for DB didnt work anymore. This fact was also the seed for No-SQL DB.

More about Big Data and non-sql here: 
http://www.kdnuggets.com/2016/07/seven-steps-understanding-nosql-databases.html

Data Science

Finally Data Science is a statistical science, which aim is to extract order out of chaos as any other science, however meanwhile the rest of the sciences are focused in a single "narrow" piece of knowledge, such as biology, chemistry, etc; data science is on the other hand multidisciplinar science that could face problems from a broaden origin. Examples would be marketing or business oriented, cosmology, etc.

So data science uses mathematical and computer science algorithms to provide some useful information out of a disordered set of data. And here is where the link with Big Data comes, actually is in the question is set before: What can he do with such amount of information he could never end to compute? So Data Science and Big data are a very usual marriage in most IT companies nowadays and in more specific fields day after day. But, data science is apply a set of mathematical algorithms to data (like apply a calculation in an excel file to create a new row) and big data is the technology to have a huge amount of excel files (I use the word "excel files" here is just to make it easier to grasp).