A union is recognized by the NLRB and has certain statutory entitlements regarding strikes and the ability for employers to fire striking workers. "Labor movements," writ large, do not require those statutory entitlements. Modern unions can be understood in terms of their ability to collectively bargain without fear of direct reprisal in terms of employment. Otherwise, collective bargaining has always been an option (it's just humans acting in concert), and long predated the concept of "unions."
I feel confident that most people would say a formal organization of workers that engaged in collective bargaining and strikes without legal protections was a union, even if it existed before the NLRB. If what you really want to talk about is "modern legally-recognized unions" then just say that.
Maybe, but when they say union membership is down, they mean NLRB recognized unions. We do not have good stats on labor movements writ large. To the OP’s post, Google’s not tackling a labor movement. They’re tackling “unions” with statutory privileges.
