Yes, this case is related to the Citizens United decision from 2010. But this Texas case shows what kind of campaign-finance laws are constitutionally allowed post-Citizens United.
Okay, to explain what happened in this Texas case requires just a little in-the-weeds review of Citizens United (and in particular what wasn’t at issue in the case). A federal law prohibited corporations and unions from spending money on “electioneering communications” to the public within 30 days of an election. This was sometimes called a ban on “independent expenditures.” What the Citizens United group wanted to do was exactly that–spend their own money to make and distribute a movie about a political candidate running for office (Hillary Clinton’s 2008 campaign). The Supreme Court held unconstitutional this federal ban on “independent expenditures” for “electioneering communications.” What the Citizens United group did not do, however, was give money directly to political candidates. And so the Supreme Court technically said nothing about limiting or banning corporate/union direct contributions to candidates for public office. In an earlier, 2003 case (Beaumont), the Supreme Court upheld a ban on these kinds of direct contributions.
Now to Texas. After Citizens United, Texas amended its own campaign-finance laws applicable to Texas corporations and unions. Texas removed its limits on “independent expenditures” (knowing that they were likely unconstitutional after Citizen United), but Texas retained their ban on direct contributions to political candidates by corporations and unions. The Texas Supreme Court last month upheld the state’s revised, direct-contribution ban against a First Amendment challenge, stating that the Beaumont decision remains valid, binding Supreme Court law, and only they can overrule it. There is, however, uncertainty about whether that will hold up.
Case: King Street Patriots v. Tex. Democratic Party, No. 15-0320 (Tex. June 30, 2017) (opinion here)