New Feature Vs Story

The answer to that question needs to come from the people that are using Jira for the work and not us. We could provide you examples of how we have used Jira but there is no answer that we can give you.  Jira is a tool designed to help organizations manage their work processes.  It was originally a ticketing system used for Help Desk scenarios but has been adapted over time for use in managing requirements for software development.  It is configurable to allow individual organizations/teams to decide how to best use it for management of their workflow. 

Start by taking Jira out of the equation and asking yourself what is the purpose of a User Story. Then ask yourself how a new feature request could be captured. After you and your team is able to answer those questions, everyone should discuss how those two "types" are defined within Jira and decide how best to use them. After you finish that discussion you will probably want to look at the Defect, Task, Sub-task, and any other item types that might be relevant to your organization.

I will warn you that some of the provided reporting will not use all of the item types so you will need to make sure that if you plan to use any of the reports, you are using the appropriate type of items.

Story is one of the default issue types in Jira Software. New Feature is a default issue type in Jira Service Management. Either may also be a custom issue type, depending on the configuration of your Jira instance. You'd have to consult your team or Jira administrator to understand the differences in configuration, such as the workflow or screens/fields associated with each issue type.