This is possible, but you have to be a little creative. You need to determine where it says "Group" then figure out how to change it. Lets start with the GroupsList. Since you have already segmented groups into types, might as well go a little further and create a new template for that type.
1) Open the Template Editor in the Control Panel.
2) Click New Template
3) Click Create a Blank Template
4) Choose Template Type: Groups
5) Choose Save to: Portal
6) Enter a template name and click save.
The hardest part is getting the default template into the new one you just created. You can get this from DesktopModules/ActiveSocial/config/templates/groups/GroupsList.ascx. Copy and Paste the default template into your new blank template and click save. Now we need to start replacing the word "Groups".
If you site doesn't support multiple languages then simply replace "[ RESX:BrowseGroups ]" with the word of your choice. You could even remove it completely if you wanted. If your site does support multiple languages then you need to create a new entry in the SharedResources.resx file using the DotNetNuke language tools.
Next we need to replace Create New Group with something more suited for the current context. [AS:CONTROL:NEWGROUP] is actually just a token for this...
<active:link text='[RESX:AddGroup]' tabid='[AS:SOCIALSETTINGS:GROUPSLISTTABID]' CssClass='CommandButton' params='[AS:PARAMKEY:VIEWTYPE]=[AS:VIEWS:GROUPADD]' visible='[AS:SECURITY:GROUP:CANCREATE]' runat='server' />
You want to replace RESX:AddGroup the same we removed Browse Groups. Simply replace it with your own text or create a new language string.
The really hard part is going to be altering the GroupAdd template. The GroupAdd Control doesn't support Social View Settings yet which means you can't have multiple templates. Your best option for this one is going to be changing the labels to be slightly more generic.