Continuous is current that runs all the time, like a motor going steady state.
Peak is a brief surge, like when the motor is just starting from a stopped state, or is running along and gets jammed up for some reason.
"why isn't 3 A peak current fit my 2.6 A - 3.0 A motor?"
because you said
current consumption is 2.6A to 3.5A
and 3 is < 3.5. Just going by your numbers.