What are fire safety concerns for cotton vs synthetic bed clothes?

Different. Synthetic clothes of any type will melt when exposed to flame, be they bed clothes or anything else. Natural fabrics tend to not burn as easily, particularly wool fabrics, which are very difficult to burn, if at all. Cotton will burn, but at least will not melt to the skin.
Fire concerns. In addition to info provided by Dr. Hines - many synthetic materials can throw off toxic fumes when burned.