On the messaging app Line, a late-afternoon conversation between colleagues might involve a series of colorful icons, or stickers — a way to invite someone out for a drink or to gently say no:

Man with a mug of beer, winking.

Bear busy at work at his desk.

Man on his knees, devastated.

Bear bowing in apology.

“They’re great when you don’t have time to type out entire messages but don’t want to be rude, either,” said Motoko Kondo, 34, who works at a Tokyo design agency. “I sometimes carry out entire conversations with only stickers.”

Line is among a growing number of apps jostling for control of the rapidly growing mobile messaging business. Such start-ups are no longer just competing for users and their time. They are also racing to define how a younger generation — one that has increasingly moved away from traditional text messaging, as well as Facebook and Twitter — will message on the go.

“There’s a frenzy of experimentation going on with the future of messaging, with new ways of communicating on mobile that go beyond typing something and hitting ‘send,’ ” said Benedict Evans, a partner with the venture capital firm Andreessen Horowitz, which has invested in social networks and messaging services.