Generally, Civ V works as you would expect it to, with the wording on details intended to be clear and provide all relevant info, that is to say, without obscuring criteria.
In this case, you get the production bonus AND the happiness bonus, as they are two discrete effects not tied together - if you only got access to the happiness bonus when you were building a wonder, it would most likely be worded in a slightly different way, such as "+15% production when building wonders and +1 happiness for every 10 citizens in a city while constructing a wonder"