For Maror there are those that use lettuce, those that use endives, those that use fresh grated horseradish, or maybe something else. Is there a difference in what you use for Maror and what you use for Koraich?
The Mishna (Pesachim 39a) lists five types of plants which are considered marror. They are:
Although various opinions have been offered to define these five species, we only use those those species which are known by tradition to be marror.
The first, Chazeres, is defined as Chasa which is commonly accepted as Romaine lettuce. Some hold that it is crisp head or iceberg lettuce. Even although it isn't bitter initially, if held in the earth for a time it becomes bitter. The Yerushalmi explains that the development of lettuce simulates the situation in Egypt, sweet at first and then becoming bitter. The Chazon Ish maintains that the lettuce must have at least somewhat of a bitter taste, other poskim disagree.
Ulshin is considered to be endives or escarole, types of chicory.
Tacha is horseradish
Charchavina and Marror, poskim hold that their definition is no longer known to us by tradition. (Pesachim 39a)
For what it's worth, here's what my family does:
For Maror, we each get a small slab of fresh horseradish, and we complete our requirement with lettuce. For Koreich, we each get a small sandwich including fresh-grated horseradish, and again complete our requirement with lettuce.
I suspect that the reason we get slabs at Maror and grated at Koreich is that the former is better for dipping by itself, while the latter sits on matza in a sandwich more readily.