In Simple, yarn is framework to manage resources, and mapreduce is framework for data processing.
Ex - if any dataset comes, it will decide to assign and de-assign the resources whereas mapreduce is use for process those data with provided resources.
YARN Infrastructure (Yet Another Resource Negotiator) is the framework responsible for providing the computational resources (e.g., CPUs, memory, etc.) needed for application executions. Two important elements are:
Hadoop MapReduce is a software framework for easily writing applications which process vast amounts of data.
Hope this helps.