The Wikipedia article on Capsicum
reads, citing a FAQ on a page of the ollege of Agriculture and Home Economics of the New Mexico State University:
Capsaicin is present in large quantities in the placental tissue (which holds the seeds), the internal membranes and, to a lesser extent, the other fleshy parts of the fruits of plants in the genus Capsicum. Contrary to popular belief, the seeds themselves do not produce any capsaicin, although the highest concentration of capsaicin can be found in the white pith around the seeds.
Cisneros-Pineda et al. measured via gas chromatography the content of capsaicin and dihydrocapsaicin in the pericarp, placenta, and seeds of seven cultivars of chili peppers and the results confirm this:
For dihydrocapsaicin, the difference is not so large, but the placenta still has a higher concentration.
In terms of concentration considering fresh mass the difference won't be as dramatic because while the seeds lose around half their mass by drying, the placenta will lose 90%.
Each variety of chile has a subtly different flavor, but generally the kind to use is determined by how spicy you want the dish to be; spicier dishes need hotter peppers, otherwise you end up with a dish dominated by the peppers. For this reason, most people sort chiles by their spiciness, measured in Scoville Heat Units (SHU). The exact same papers can be used for Mexican and Indian cooking, as long as you want similar spiciness.
To give options, I like to keep 3 kinds of dried peppers: a mild paprika, a standard hot pepper, and a ground, smoked one. The sweet paprika is for savor, the hot pepper to add spiciness, and ground, smoked peppers bring that distinctive smoky flavor to dishes. I usually use de Arbol pepper flakes (about 30k SHU) to add heat, and smoked hot paprika for smoked stuff. When I have a dish that showcases the flavor of a specific pepper, it's time to get fresh ones from the store.
For general purpose cooking, many people use mild paprika to add sweet, smoky flavors to Italian, French, Spanish, and Balkan cuisines. Generally these are of the Capsicum annuum species.
Indian, Szechuan Chinese, and Central American cuisine normally use moderately hot peppers, in the 10-30k SHU heat range. Cayenne, tabasco, and de Arbol peppers are good examples. Thailand (and some parts of India) use very hot peppers up to 100k Scoville, called Bird's Eye or Thai chiles. These peppers may be either Capsicum annuum (normally milder) or Capsicum frutescens (normally hotter).
Finally, Mexico and northeastern India use the hottest peppers of the Capsicum chinense species, including habaneros and the naga jolokia, which go from 100k SHU to 750k SHU.
Mexico is a special case, because many varieties of pepper are mixed to get the desired flavor. Everything from bell peppers to habaneros gets regular use, and may be used smoked or dried.
Best Answer
This isn't a definitive answer, but I suspect that the name you have for it is the english name. There are many many varieties of chili and many of them are not found in the english speaking parts of the world, so the local name is the english name.
I googled the name as you provided it and found that it probably is called an unhelpful "green chili". It is very probable that the "morris" part is a corruption of "morich" which translates to pepper (see the entries for morich on this list of Bangladeshi spices). Within that list is an entry for "green chili pepper" which has the local name of "kancha morich" or "kancha lonka", which seems to be a variant name with associated recipes.
I have been unable to find a Scoville rating for this chili or even which of the species of Capsicum it is, but the rating is normally done on dried chili (I think!). There is an excellent summary of chili varieties and types in this page, which might give you some direction.