Often, the 'line' is just decorative. It's meaningless.
In rooms where it's meaningless, or not there, motion past the cards is the "forward motion" that is looked for.
Also, in some rooms, forward motion means that the entire stack in the player's hand is the bet. But most rooms allow the motion followed by cutting a portion to make the bet, bringing the remainder back.
Bottom line: They are both subject to 'house rule', which can be different for cash vs tournament.
In either case, the key is to watch for a delay between making stacks, or backward motion followed by another forward motion. That's always a string bet.
On a side note, what's the purpose of the line in rooms where it's meaningless?
It's so the maintenance guy who changes the felt can measure and make sure it's correctly positioned.