Subspace can be thought of as containing domains. Each domain of subspace is an infinite space adjacent to our own with different physical laws. In essence, each subspace domain contains its own universe. Our own universe exists within our own subspace domain.
Each domain is like a single cell in a beehive, subspace exists in layers, each layer is believed to have an infinite number of domains with in it. Each layer exists parallel to the layer our own universe exists in. Subspace particles can travel into subspace to varying depths, traveling deep enough into subspace transitions between our own subspace domain into other domains. Furthering the analogy, subspace particles with enough energy and variance from our own can also travel between subspace layers.
Dimensional Fold Drive
The DFD creates a pocket of reality between subspace domains. Within this artificially created sub-domain the engines field alters the physical laws connecting that pocket to reality an thus allows faster than light travel, travel through time, and other potential benefits.
Hyperspace is, itself, a subspace domain within our own layer of subspace. Existing parallel and very close to our own domain, connected to our own domain, but also existing unto itself entirely.