Discussion Groups / ESL Teaching / May 2006

It varies (eg British English / American English). Capsicum is the
genus, part of the plant's official Latin name.

The fruit of Capsicum plants is commonly called 'chile pepper' or just
pepper in Britain and the US, but is usually called 'capsicum' in
Australian English.
  In Australia and New Zealand, heatless species are called "capsicums"
while hot ones are called "chilli/chillies" (two L's). The term "bell
peppers" is rarely used, usually in reference to C. annuum and other
varieties which look like a "capsicum" or bell but are fairly hot. A
common Australian mispronunciation is "capsicun."
  In the United Kingdom, Ireland, and Canada, the heatless varieties
are called "peppers" or "sweet peppers" (or "green peppers," "red
peppers," etc) while the hot ones are "chilli/chillies" (two L's) or
"chilli peppers".
  In the United States, 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).

taken from:
http://en.wikipedia.org/wiki/Capsicum

"heatless" in the above means "not hot" and refers to the big, fat,
round ones.

Owain