I am trying to explain to best of my knowledge and from Pega Help.
Work Class - Contains the rules that describe how to process a case, such as processed, date element and user interfaces.
Data Class - Contains the rules that describe the data objects used in application, such as a customer or collection of order items.
These activities apply to the @baseclass, Work-, Assign-, and History- classes.
Use the Security tab to specify the activity type and optionally to restrict which users (or other requestors) can execute the activity. This optional security supplants restrictions based on RuleSet and version.
You can specify zero, one, or more than one privilege to restrict access. Order is not significant. At runtime, any match between a privilege listed and those a user possesses allows users to execute this rule.
Allow direct invocation from the client or a service
Select to allow users to start this activity directly through user input processing, for example through a Submit button or a pyActivity= element in an URL. Clear this if this activity is to be started only from another activity, through a Call, Branch, or other means.
For example, select the box for a service activity, or if this activity is called by an AJAX event from a form.
At run time, if the box is not selected and a user attempts to start this activity by user input, the activity does not run and returns a method status of Fail:Security.
For most activities, leave this box cleared to promote security of your application. Unless needed by your design, allowing activities to be started from a URL or other user input — whether the requestor is authenticated or a guest — may let users bypass important checking, security, or setup.
Require authentication to run
Select to require that only authenticated requestors can start this activity.
Clear to allow guest users to run this activity, if they meet other security and access criteria. Guest users — unauthenticated requestors — typically have access to rules in the RuleSets provided in the PRPC:Unauthenticated access group, as referenced in the Requestor type instance namedpega.BROWSER.
If you update the BROWSER requestor type to reference a different access group, or update the PegaRULES:Unauthenticated access group to make additional RuleSets available to unauthenticated users, review carefully this check box for each activity in the RuleSets. Select this check box for all but those specific activities that guests need to run.
In most cases, clear this check box if the activity is for an agent. Agents are not true authenticated users and by default cannot run activities that are restricted to authenticated users. However, this check box is ignored by agents for which the Bypass activity authentication check box (on the Security tab is checked; they can run activities regardless of the Authenticate? value.
Identify privileges in this array to restrict which users and other requestors can execute this activity. At runtime, if the user does not possess an access role that — through an Access of Role to Object rule — provides access to one of the identified privileges, the execution of the activity fails.
Privilege Class Optional. Identify the Applies To key part of a class to use at runtime to locate a privilege rule. Normally this is the same as the Applies To key part of this activity.
Optional. Identify the name for a privilege in that class (or an ancestor class). The class you enter and the name must together identify a privilege (using rule resolution including class inheritance.)
So in short it really depends on which user to want to give access to and who/how you want these activities to be invoked.
Let me know if this helps, if you have any query you can post us.