Okay, so I just realized you were using Zoo Visitor. As @Derek Hogue, User by Solspace will handle this for you, or as I mentioned, hidden input fields on custom, but separate forms will work.
But Zoo Visitor allows for selection of user groups. I believe it also takes care of people trying to add themselves to SuperAdmin but you should also be able to strengthen the backend protocols so that only SuperAdmins can modify the SuperAdmin group. See this code from Zoo Visitor
{exp:zoo_visitor:registration_form error_handling="inline" return='account/register/success' allowed_groups="5|6"}
Select member group:
<select name="group_id">
<option value="5">Group with id 5</option>
<option value="6">Group with id 6</option>
</select>
Email*: <input id="email" name="email" type="text" value="" />
{error:email}
Password*: <input id="password" name="password" type="password" value="" />
{error:password}
Confirm password*: <input id="password_confirm" name="password_confirm" type="password" value="" />
Member firstname: <input id="member_firstname" name="member_firstname" type="text" value="" />
{error:member_firstname}
Member lastname: <input id="member_lastname" name="member_lastname" type="text" value="" />
{error:member_lastname}
<input class="form-submit" type="submit" value="Register" />
{/exp:zoo_visitor:registration_form}
It's the Select member group section, you are interested in:
<select name="group_id">
<option value="5">Group with id 5</option>
<option value="6">Group with id 6</option>
</select>
Here's an example with a hidden member group
{exp:zoo_visitor:registration_form error_handling="inline" return='account/register/success' allowed_groups="5"}
<input type="hidden" name="group_id" value="5">
Email*: <input id="email" name="email" type="text" value="" />
{error:email}
Password*: <input id="password" name="password" type="password" value="" />
{error:password}
Confirm password*: <input id="password_confirm" name="password_confirm" type="password" value="" />
Member firstname: <input id="member_firstname" name="member_firstname" type="text" value="" />
{error:member_firstname}
Member lastname: <input id="member_lastname" name="member_lastname" type="text" value="" />
{error:member_lastname}
<input class="form-submit" type="submit" value="Register" />
{/exp:zoo_visitor:registration_form}
Please take note that, I also limited what group_id could be used in the form. I believe Zoo Visitor uses this as a security check, incase the registrant tries to manually supply a different member group, like group_id="1" which would make them a super_admin.
When duplicating the form, you would need to change both the allowed group and the hidden field value.