score:6
First things first. The page you found via a Google search contains old, out-of-date information. Namely, it addresses the rules prior to 2014 and does not account for the rule changes that became active in April 2015. And they don't even get the old stuff from pre-2010 right! Finding old information or old attestations from discussion forums are a damning factor where UK visas are concerned. Avoid it, the net is not necessarily your friend.
In the prior regime there were categories of visitor visas called "Business Visitor", "Family Visitor", and "General Visitor". People were finding these rules unfit for purpose and the Home Office opened a private consultation with the UK legal community and this gave birth to a new set of rules. The new kind of visa is called "Standard Visitor Visa".
There were lots of changes but the biggest changes affecting you are...
I wanted to travel around after the interview as well
That's wonderful, they like it because tourist revenue is a vital part of the UK economy (and Parliament relies on British missions abroad to help make this happen). Consulates are supposed to issue as many visitor visas as they can (subject to the applicant's suitability). So write it down on your application.
My question was meant to be more like are all visas given for 6 months?
They try very hard to be uniform about it and give everyone 6 months. Issuing a lesser period is possible but they have to change the machine and run a single passport through it and then reset it again and this invites mistakes and similar operational problems. That's part of why they 'standardised' it.
Or is it possible that the visas might be given for just the duration of travel based on air tickets?
Bzzzzzt! Wrong. They don't want to see air tickets during the application stage. Read the guidance. And stay off the net :)
From the "gov.uk" domain...
The Guidance