Are map reduce and pig similar in the programming?

no, 

PIG is a scripting language which gets converted into mapreduce while the programme is running on hadoop

Lets look at the definition on Hadoop for PIG :

A high-level data-flow language and execution framework for parallel computation.

and in here :

Pig's infrastructure layer consists of a compiler that produces sequences of Map-Reduce programs

so we can tell that Pig is an abstract over map-reduce.

I concur with Mohsin.

MapReduce programming paradigm is precisely & purely written in Java and more suitable for core data design programmers. Pig is like an abstraction for MapReduce where the core programming concepts are not involved in designing the programs. It is designed in such a way that a non programmer can also write a MapReduce program without actually knowing the basics of it. Pig is mainly for Data Analysts & Architects.

Yes, Pig Internally create list of map reduce jobs and run one after another.  

They are not similar.  Pig is like a high level language which is internaly coverted to map reduce on hadoop.