also in re: "functional" any kind of training has some kind of goal in mind, which may be more or less specialized
i.e. endurance athletes (runners, cyclists) do very specific training that makes them extremely good at their discipline but not very "overall fit" if that's taken to include strength, explosiveness, etc
powerlifters would be at the other end of the specialization spectrum, incredibly strong, no endurance
Crossfit - and any other high-intensity interval training (HIIT) - is about splitting the difference to optimize overall fitness, i.e. a true specialist should be able to outdo a CF person in that specialty but in a general competition - i.e. the Crossfit Games - including many elements of fitness the CF person should prevail. in practice, a ton of high-level CF people also have a background in gymnastics or Olympic weightlifting or what have you.
construction is likely closer to general fitness, depending on what exactly you're doing - where it does have an advantage over the gym (as a person who's spent years doing a physical job) is in conditioning you to the mental/physical fatigue of full 8-10 or whatever hour day, whereas the gym for anyone who's not a personal trainer/gym owner is about getting the most you can out of the limited time you have available
also - I always distinguish between capital-C Crossfit the business entity - Reebok, ESPN, affiliates, etc - and the lower-case crossfit as an approach to fitness, which is similar to any other kind of HIIT approach