When you add a new column to a Sharepoint list you can decide for the new column to be a lookup field to a different list.
By default the lookup will show the title of the list item in the lookup list. When adding the column (either via the web or programmatically) you can lookup to a field other than the item's title. However,
Look up fields will only reference fields that are of type "Single Line of Text". You can in code set them to other field types, such as DateTime fields, but Sharepoint will ignore this and default to Title.
There is a bit of a hack around where by you fool Sharepoint into looking up to a different field type. You create the column as a single line of text, create a lookup to it then change the target field from a single line of text to the data type you require. I wouldn't advise this though, it is unsupported and it is best to treat the column you are adding as the data type it represents, also doing this programmatically is a real Kludge!