Is it true: regardless whether condo or co-op, both types of living units share laundry room?

Not necessarily. A condo is a private home and most do have their own washer and dryer. However, there are some that use a laundry room and may have a HOA agreement to not install individual washers and dryers. This is mostly with old apartment buildings that have been converted to condos. In some cases the building code may not allow the plumbing for individual washer and dryers. New condos are specifically build. In other words, it may seem simple, but it's like trying to build a new shower and bath room in some apartment building.