One issue is that in Drupal, there isn't really a division between front-end and back-end. The whole idea of an administration theme in Drupal is relatively new, and the default prior to Drupal 7 was that settings forms would look no different than content pages.
Meanwhile, WordPress (and, to an even larger degree, Joomla!) has a clear delineation between front- and back-end. CiviCRM's main interface (the part for trusted users to see other contacts' stuff) is considered a back-end feature, and you have to access it via the WordPress administrative menu.
(That said, at least in WordPress it's a relatively smooth process to get to the back-end. In Joomla! the login sessions are independent.)
To accomplish what you need, create a dummy user to serve as a prototypical case manager and do the following:
If you haven't already, install a role editing plugin for WordPress to allow you to define a new role for case managers.
Go to Administer > Users and Permissions > Permissions (Access Control) in CiviCRM and then click WordPress Access Control.
You should see a column for your newly-created role with a bunch of checkboxes. Each row is a separate capability within CiviCRM, and by default, your new role will have none that are special. You may need to experiment a bit with granting capabilities, but the ones I know you'll need to grant your new role are:
Most permissions have a description (shout out to Jane Hanley and Tommy Bobo for actually documenting all of them at a code and documentation sprint), so you can get an idea of what others you should grant. Unless you grant specific ACLs (see below) for your users, for example, you'll probably want to also grant
CiviCRM: edit all contacts and
CiviCRM: view all activities to your role.
Use the "Private Browser" feature in Firefox (or "Incognito" feature in Chrome) to log in as that prototype user. See if the permissions seem correct for that sort of user. If not, go back to the WordPress Access Control page as an admin and adjust accordingly. (When you, the admin, grant or revoke capabilities, you, the case manager user, should probably log out and then back in to make sure the permissions are working correctly.)
If you want to set up detailed permissions over subsets of contacts, fields, etc., you'll need to use CiviCRM ACLs to grant access. Permission is additive, so if, for example, a user has the
CiviCRM: edit all contacts capability, the ACLs for editing contacts will have no effect since that permission is already granted across the board.
Finally, check out the CiviCRM User Guide page for Permissions and Access Control for a more thorough guide to this.