What is the difference between deploy and deploy and persist model for machine learning models?

Answer:

Deploying a machine learning run will load the results of that run into your data model, feeding any metrics, dimensions, and columns created for reporting on this data. Storyboards created from machine learning data are generally configured to display the most recent deployed run and should automatically refresh after your site has been processed. 

Deploy and persist model is different in that everything described above happens but the predictive model is also “frozen”.  After persisting a model, a new model will not be trained on subsequent runs.  Instead, the existing model (algorithm, settings, features, etc.) will be used.  The only thing that may change is the data you’re making predictions on.  Models that have been persisted can be unpersisted if you decide you want to train a new model by selecting the “Unpersist Current Model” button.

Deploy or Deploy and Persist ML Models from the Results Summary