You heard correctly. They concern different aspects of the use of language.
The expression "Anorak" refers to an introverted perfectionist or pedant [British train-spotters are generally assumed to wear anoraks, as do computer geeks], so in saying "Get away from the Anorak language..," Chris Patten means that he does not want to be tied down by narrow definitions of what his job entails.
"Management Goulash" refers to what is also known as "management-speak", which applies to people using words and phrases which they think make them sound well informed and important, rather than using simple, straight-forward words. For example, such expressions as "a holistic, cradle-to-grave approach", or "paradigm shifts", or "stakeholders" are heard all too often. Chris Patten's official job specification will undoubtedly be well laced with that sort of rubbish, and he wants to explain his role in simple terms.
The major difference in their accents is that Chris Patten has an English accent, while Andrew Marr has a Scots accent. Both men are instantly recognisable from their speech as being well educated, sophisticated individuals.