I was just wondering what you all consider to the roles of these two positions in the modern game. Growing up, I always considered the 7 to be the organiser - someone who takes the game by the scruff of the neck and controls it for 80 minutes at first receiver. The Stand-Off was always the second receiver a couple of players wider than the 7 and was someone who could make something happen through a little bit of individual brilliance.

However, in the modern game the two roles seem to be practically identical. What do you want to see from a Half Back partnership in the modern game?

In the modern game i think that the Scrum half is more of a runner and plays a bit more off the cuff where as the stand off is more of an organiser and does more of the kicking.

You are both right, the third option being one plays left and one plays right

I still see the 6 as the runner (McGuire, Pryce) and the 7 as the schemer, organiser and short kicking game general (Long, Goulding). Obviously it doesn't particularly matter which one does which provided you've got both in the side.

We have only played with 1 at Cas lately and now it will be none.

At Wigan, we seem to do the opposite. Smith is the general organiser & kicker, Green does the running, off the cuff stuff and then Tomkins sweeps around as an extra option also.

Like most questions, the answers is: It depends.
They might play left and right.
They might play first (close to the PTB) and 2nd receiver (out wide)
In either case, either player could be the "boss"
With a great SO, the SH might just be there to organise the little stuff while the SO sets up the wide play, and then act as a link to the SO. Or vice-versa, and the SO might just be an outlet or decoy for the SH.
Then you could bring in a playmaking fullback, or loose forward.

Or even a hooker, a la Brad Drew.

Theres so many different combos that you could use, though I suppose traditionally I would consider the 7 as the conductor and the 6 as the silky skilled half back role.

both 5/8ths now look at the opposition and try to place themselves in the attacking line up to exploit the weaker defenders to try and make a line break or pull a 2nd defender in to cover and thus creating an overlap. The coaches analyse the opponents and with the playmakers of their own team (1,6,7,9,13) formulate a plan A,B,C. even in the same game you will find that the 5/8ths often change their style and positioning of attack to exploit weaknesses.

Stand-off hides down the left-centre channel/left wing on defence, scrum-half on the right.

Only the stand off is (to use the aussie parlance) a 5/8, so named as he will stand five eighths of the way back between the scrummage line and the last man (the full back). Scrum half is a half back, standing half (or 4/8ths) of the way back. Similarly the wingers and centres stand 3/4 of the way back and are called threequarters and the full back stands the furthest back so is all the way (full) back. That is how the positional names came about during the formation of the game in the 1800s.

As others have said different teams will apply different formations and give different roles to their SO and SH dependent on what the skill set and strengths of those individual players are. There no longer is a specific fixed role for either position as their roles are largely interchangeable.

It's all dependant. If you look at Warrington, its a left and right split. Yet if you look at Saints a few years back, it was very much half back and five eigth with Long and Pryce. I suppose it depends on the talent you have available and the coach. Old school five eights are drifting slightly out of the game, especially over here, yet the best team in the world use that system with Cronk and Widdop.

Balance.

As long as between your half backs you have all the necessary skill set covered (running threat, passing game, game management, field kicking) it doesn't really matter which one does which and what number they have on their back.