Samir is right, but there are now many flavors of Hadoop, (hortonworks being one of the original and Free versions), MAPR makes a unique version that is very fast but there are also many other free analytic tools that can layer on top of hadoop. Big data must scale and MongoDB through shards also supports this and many businesses have adopted this model. Hadoop does stand as king since the largest sites eg. Yahoo and others are using it. There however are many recipes to the ideal solution depending on your needs and data sources (plus budget).

Working with Big Data is definitely one of the most powerful things to learn and deploy as a skill in present scenarios. Specialists are adopting the skill to work with Big Data becuase it is one of the most challenging and interesting skill to have which is even on a high rise demand. Then I must add to it that Hadoop is one of the skills we can use to work with Big Data and so are many others like NoSQL databases for storing, Map Reduce programming, Pig, PLATFORA, Sky Tree and many more. So definitely Hadoop and Big Data are not synonyms but rather it is one of the most sought after skill to posess in the Big Data era.

I do not think they are but Hadoop skills could give you value in this era of big data (as mentioned by Satyajit)

- Big Data is the huge mass of data that can't be processed easily on one regular machine.

- Hadoop is a framework for parallelizing the process on big data.

Of course Hadoop and mapReduce is not the only way to deal with the big data. Not always we can parallelize the algorithm and run on the cloud.

There are other methods for Big Data Analytics like indexing, data patritioning and clustering that work well depending the case.

Big data is simply the large sets of data that businesses and other parties put together to serve specific goals and operations.Big data can include many different kinds of data in many different kinds of formats.

Hadoop is one of the tools designed to handle big data. Hadoop and other software products work to interpret or parse the results of big data searches through specific proprietary algorithms and methods. Hadoop is an open-source program under the Apache license that is maintained by a global community of users. It includes various main components, including a MapReduce set of functions and a Hadoop distributed file system (HDFS).

Hadoop is not a synonym for big data. 

Hadoop is a technological tool, just like its relational database counterparts. On the other hand, big data is not about technology, but rather about business needs. This means that Hadoop shouldn’t be considered as the sole player in the field of data analysis. For example, it makes sense to use Hadoop to run broad exploratory analysis of large data, but a relational database is still a better option to perform an operational analysis of what was uncovered. Hadoop is also good for looking at the lowest level of detail in a data set, but relational databases make more sense when it comes to storing transformed and aggregated data. 

No,

Hadoop is not at all synonym to Big Data.You can see it like this - Big Data is a Problem and Hadoop is a solution to it.

Big Data simply means a huge amount of structured and unstructured data generated in high volume, variety and velocity.

Hadoop is a framework to manage this Big Data through it's three main components:

So, they are definitely not synonyms to each other. You can read more on Apache Hadoop from this link - https://data-flair.training/blogs/hadoop-tutorial/