Convection heating warms the air. A boiler or fan heater pushes hot air into the room, the air rises to the ceiling, and you wait for enough of it to circulate back down to where people are sitting. In a church with a high vaulted ceiling, that means heating a vast volume of air that nobody occupies. It is slow, expensive and the warmest spot is usually fifteen metres above the congregation's heads.
Infrared heating warms objects and people directly, the same way the sun warms you on a cold day. The energy travels in a straight line from the heater to whatever it hits. Surfaces absorb it and re-radiate gently, so the pews, the floor and the congregation feel warm without the air temperature needing to rise much at all.
For churches this difference is decisive. You get warmth in minutes rather than hours, you stop heating unused air volume, and you avoid the cycling of hot, dry air that can crack historic woodwork and dry out lime plaster. Infrared is also silent, which matters more than most people realise until they have sat through a service with a noisy gas blower running in the background.