Sorry, I’m not familiar with how your other keyboard did it, but in either the Motif (2001) or the Motif ES (2003) you have several ways to approach it.
You could record a User Arpeggio. The instrument’s Sequencer is used to create the phrase (run) you can then convert this phrase from the Sequencer Track to a User Arp. The User Arps (256) can be assigned to any Voice or Part, and can be set to trigger from any Note or Note Range, any Velocity or Velocity Range, and it can be set to Loop or play once when triggered. Over the past two decades the Yamaha Arpeggiator has expanded and reinvented the possibilities of this function.
Both the Motif and the Motif ES are samplers, which means you can sample (record) any run and assign it to playback from a note-on event. A Drum Kit Voice can hold as many as 73 Audio Waveforms... Waveforms can hold different phrases so that you can trigger different phrases from a single Key at different velocities. And again they can be set to Loop or play once when triggered.