What material is used for inflatables?
PVC and vinyl are both abreviations for PolyVinylChloride. Inflatable float toys and furniture were normally made of plasticised PVC film. In the past the plasticiser tended to leach out giving an intense odour when the item was new and resulting in toys losing their "bounce" after 1 season of use. Modern toys seem to be made of better quality materials.

PVC can be joined using heat but it is difficult and most commercial production is done using HF (radio frequency electric) welding. For hobby purposes solvent welding (glue) may be considered. It is slow though and requires constant pressure while it sets. 

It is possible that other polymers may replace PVC, there has been a push to reduce chlorine use in plastics.

The large inflatables like "bouncy castles" are almost certainly made from polyurethane reinforced with a cloth typically nylon. Since these are usually supplied with air constantly they need not be airtight, and may be joined by stitching. Polyurethane can also be joined by HF welding where airtight joins are needed.