Some search for a massage armchair, others for a massage chair or seat. Shops use all three names for the same devices. Short answer: it is usually the same thing. The longer answer is below.
Manufacturers and retailers use several names for the same product, so when browsing it is worth checking more than one term — the difference is often in wording, not in the devices themselves.
One exception: vibrating seat pads and office chairs with vibration are sometimes also called massage chairs. They cost a few hundred euros and have little in common with a full-size massage chair, which has a roller mechanism, a back track and a leg massage section. If the price looks too good, it is probably not a real massage chair.
Mechanism: 2D rollers move in two directions, 3D adds depth, 4D also varies rhythm. Track: an SL-shaped track covers the back from neck to thighs. Zero gravity: legs raised above heart level let the massage work deeper. Dimensions: a reclined chair needs more space than it seems — check the specs of each model.
Whatever you call it, what matters is the mechanism, the track and the size. Compare all iRest models by these criteria.