Can braces add space to your teeth or do they just bring them together?

Within limits: Orthodontic treatment can change the relationship of teeth and bone support (jaws) to each other. Space can be opened ore closed, as long as there is sufficient jaw bone to support the teeth. See a qualified orthodontic specialist for an evaluation.

They do both: You can close spaces or increase space with braces and invisalign.

Open spaces: Orthodontic treatment are often designed to open spaces in specific locations for reasons. For instance, space may be required to insert a replacement tooth or implant or a tooth backed-up to open space for a dental bridge. Consequently, spaces between teeth can be maintained, opened, or closed.