Most locks just don't have the much-vaunted "one position sear", so there will be a difference in how much room there is between the trigger and sear at half cock and full cock. When you have the lock screws tightened, you should have just the smallest amount of slack between the trigger and sear at half cock. Almost bearing on it, but not quite. If you get it too tight, as the wood expands and contracts, you'll probably end up with the trigger not allowing the sear to go fully into the half cock notch, so you gotta have some room. At full cock, the sear is generally not as low as it is at half cock, so there will be more of the dreaded "slop", that so many people today simply cannot stand. With the cock down, it doesn't really matter much if the sear is on the trigger or not.
Now, the half cock is NOT A SAFETY.
let me repeat THE HALF COCK IS NOT A SAFETY
If you pull hard on the trigger at half cock, it probably will force itself out of position (and possibly damaging the sear and half cock notch in the process). Don't do it.