Not quite sure what you mean by a different way, or sequencers author. Do you mean the musician, or like Roland/Korg/ARP?
MIDI is a pretty exact specification. If a sequencer is changing the timing of anything, the underlying MIDI structures are not the same then. You can have different amounts of swing or different PPQ values, but then I wouldn't consider that "the same MIDI".
You can feed it to different sound generators of course, different drum machines, synths, a laptop, what-have-you, (most sequencers have both builtin together) but that's different from the MIDI itself.
Given a specific MIDI file, with specific applied quantization, they should absolutely play the same way -- the only exception is the timing resolution they offer and smallish latency issues (which in practice should be 100% transparent).
MIDI is a pretty exact specification. If a sequencer is changing the timing of anything, the underlying MIDI structures are not the same then. You can have different amounts of swing or different PPQ values, but then I wouldn't consider that "the same MIDI".
You can feed it to different sound generators of course, different drum machines, synths, a laptop, what-have-you, (most sequencers have both builtin together) but that's different from the MIDI itself.