is reconstitution solution the same as bacteriostatic water?
Short answer as far as I can tell: sometimes, and you can't tell from the name.
"Reconstitution solution" describes a purpose, not a composition. Products sold under that label vary. Some are bac water under a different name, some contain other preservatives, buffers or excipients.
So the question can't be answered in general, only by reading the composition of the specific product. Which means the useful habit is to ignore the product name entirely and look for the ingredient list. If there isn't one, that's the answer to a different and more important question.