local[*]
This is specific to run the job in local mode
Usually we use this to perform POC's and on a very small data.
You can debug the job to understand how each line of code is working.
But, you need to be aware that since the job is running in your local you cannot get the most out of sparks distributed architecture.
yarn-client
your driver program is running on the yarn client where you type the command to submit the spark application . But, the tasks are still executed on the Executors.
yarn-cluster
In cluster mode, the Spark driver runs inside an application master process which is managed by YARN on the cluster, and the client can go away after initiating the application. This is the finest way of running the spark job to be benefited by the advantages provided by a cluster manager
I hope this gives you a clarity on how you may want to deploy your spark job.
Infact, Spark provides you a very clean documentation explaining various deployment strategies with examples.
https://spark.apache.org/docs/latest/running-on-yarn.html