A Social Group is a space-like container that does not fit hierarchically into the space structure. Social Groups also allow for front-end user management for permissions to the content in the social group.
A jive group most likely refers to a permission group (or user group) that can be assigned permissions to spaces from the admin console.
Harpreet if you are seeing these mixed descriptions in Jive documentation please raise it in the Documentation space - or is it a group =) where the doc team can make corrections.
For 'Jive Group', if it is in the context of granting read access permissions to a space then I personally would stress ACCESS group, such that 'group' means a SOCIAL group.
Note that *access* groups currently can't be used where you might like to for: author access to content, DMs, Shares, (social) group access etc.