As with most of these position-specific questions, much of it can depend on the personnel available and the coach in charge.
I know I often bring Briers up on these threads, but he is probably one of the few remaining quality 'traditional' stand-offs playing in SL.
In basic terms, often they will be 2nd receiver on attacking plays and will link with the wider players (usually centres, fullbacks and 2nd rowers). They will often have plenty of assists as they will be responsible for putting players through the gaps (watch Briers' pass to Atkins on Sunday for a perfect example of why I like watching Briers).
Defensively I disagree with Matt slightly in that often we see halves (6 or 7) defending in either the wing or centre position, often due to their lack of size and to protect them for their offensive play.
As you mentioned in your opening post though Cofi, often teams will use their 13 or 1 as a playmaker and he will do things which often get thought of as a 6's job. Mathers has been linking into the Wire line a lot recently and using the cut-out pass to the winger. For me, this is a bonus play and simply increases your options. Wigan on the other hand use O'Loughlin as their ball handling 2nd receiver (his number of assists this year is very impressive), and the reason I think he is 13 rather than 6 is due to the lack of pace. When it comes to the running plays etc. then Tomkins will step in.
I know this is a rambling post, but I think it highlights the difficulties in stereotyping the modern RL player, and is a reason why it can be difficult to compare like for like.
Pryce, Briers and Tomkins for example are three quite different stand offs.
Pryce, Briers and Tomkins are different players with the same number on their back. However, the teams all have the same method in mind as do all teams currently. Work the middle third and try and get a numbers mismatch on the fringe for a leader runner / sweeping second man play.
Pryce has Wellens has a full back so he can be the second option.
Briers and Tomkins have quicker full backs so they do the pass.
Essentially the number on a players back is irrelevant, it's the jobs they are asked to play that are important and how that job fits in with the next guys job. Where we can beat Australia is our 'ability' to play away from the gameplan. This is however, our downfall, too.