Actually, a horse can have laminitis without founder. Not likely, but possible.
Here is a good description:
Laminitis is defined as an inflammation of the lamina of the inner hoof wall. Laminitis and a process called founder are often thought to be the same problem. Laminitis is due to the metabolic changes that affect the lamina. Founder is the mechanical displacement of the coffin bone with in the foot. Founder is associated with laminitis but it is possible for a horse to have laminitis without founder.
George the pony has no discernable rotation of the coffin bone, going by x-rays. I guess I've always caught it early enough that the damage was kept to a minimum.