Original: In the United States and Canada, the common heatless species is referred to as "bell peppers," "sweet peppers," "red/green/etc peppers," or simply "peppers", while the hot species are collectively called "chile/chiles," "chili/chilies," or "chili/chile peppers" (one L only), "hot peppers", or named as a specific variety (e.g., banana pepper).
Simplified: In the United Kingdom, Ireland, and Canada, the heatless varieties are called "peppers", "sweet peppers" or "capsicums" (or "green peppers," "red peppers," etc) while the hot ones are "chilli/chillies" (double L) or "chilli peppers".