Is there a type of tree that produces both Hard Wood And Soft Wood (I have been watching someone play Animal Crossing)?

yes, balsawood is a soft wood hardwood

spaces and hyphens matter

trees are classified as hardwood or softwood by type of tree, so a tree cannot be both.

wikipedia:

It is common to classify wood as either softwood or hardwood. The wood from conifers (e.g. pine) is called softwood, and the wood from dicotyledons (usually broad-leaved trees, e.g. oak) is called hardwood. These names are a bit misleading, as hardwoods are not necessarily hard, and softwoods are not necessarily soft. The well-known balsa (a hardwood) is actually softer than any commercial softwood. Conversely, some softwoods (e.g. yew) are harder than many hardwoods.