Minecraft wiki entry for Death_messages, associated text: <player> went up in flames
Appears when the player is killed because they were in a fire source block.
<player> walked into fire whilst fighting <player/mob>
Appears when the player is hurt by a player or mob then entered a fire source block.
<player> burned to death
Appears when the player is killed because they were on fire, but not in a fire source block.
Also appears in the game's log when a named snow golem dies because of being in a hot biome.
<player> was burnt to a crisp whilst fighting <player/mob>
Appears when the player is hurt by a player or mob then killed because they were on fire.
Also appears in the game's log when a named snow golem is hurt by a player or mob then dies to the heat in a hot biome.