An Air Carrier pilot reported they had to abruptly stop while taxiing to avoid another taxiing aircraft.

Narrative

For departure out of LAX; we were pushed back out of Taxiway C-9 alley tail south onto Taxiway C; facing C-9. When ready to taxi; Ground gave the instruction Aircraft X; taxi Charlie-9; Bravo to Runway 25R; give way to Aircraft Y. Aircraft Y was taxiing south on Bravo north of C-9. We were both under the impression from those instructions; that we would turn on C-9 and follow Aircraft Y south on Bravo. As Aircraft Y approached C-9; we began taxiing to flow in behind them as they passed. As soon as we started moving (10-15 feet; 3-5 knots); it became apparent that Aircraft Y was turning left on to C-9. I immediately applied the brakes to stop to stay clear of C-9. At that speed; the aircraft came to stop pretty abruptly with a jolt. I knew we needed to talk to the FAs (Flight Attendants) before moving again. They called up before I called them and said that they were bumped against the walls from the jolt. The number 1 had a tingling in their arm. They said they would confer and call me back. After a minute; they called back and said they were good to continue duties. We continued the flight uneventfully.The instruction provided by Ground were vague given the situation. There was no information provided that the Aircraft Y was going to do anything other than what it was currently doing; which was taxiing south on Taxiway Bravo. We made assumptions on what the other aircraft was doing by the simple instructions provided.ATC should provide conditional taxi clearances in a clear and concise manner. Especially when directed to give way to another aircraft; it is reasonable to assume that the aircraft will continue doing what it is currently doing unless given information to expect otherwise. In this case; changing the clearance to "give way to Aircraft Y at C-9" would have prevented any confusion."