It is not clear if the shooter was killed or is the wounded man.
The gunman was being watched by members of the church security team because of his appearance, said Mike Tinius, church elder.
Witnesses said the shooting occurred as the communion was about to end Sunday morning.
The gunman died right at the scene, while another person could not survive their injuries en route to the hospital.
Wilson, who was a reserve sheriff's deputy and a firearms instructor, took the gunman down with one shot from his SIG P229.
Beto O'Rourke, the former Democratic presidential hopeful who has spoken out against gun violence in the past, tweeted that he was saddened to learn about the shooting and said, "Clearly what we are doing in Texas, what we are doing in this country, when it comes to guns is not working".
"After he shot Richard and Tony, he started towards the front of the sanctuary and that's when I was able to engage him", Wilson said to reporters.
Two people were shot dead on Sunday morning during a church service in White Settlement, Texas, before the attacker was shot and killed by two members of the church's security team.
His beard and the hair on his head looked fake, and he made her uncomfortable, Arreola said.
When will The Mandalorian Season 2 be released?
Favreau's announcement comes on the heels of The Mandalorian Season 1 finale , which aired yesterday. However, Favreau has previously indicated that he plans to direct at least one season 2 episode .
A shooter at a church in White Settlement, Texas, was taken down by parishioners with guns seconds after he began firing Sunday. Gov. Dan Patrick said in a press conference December 29 that thanks to that law, an "untold number of lives" were saved. "It was called 'Leaving a Legacy, ' and two men today left a legacy".
Tiffany Wallace talked to KXAS-TV Sunday hours after the shooting, saying her father was a deacon and lifelong membver of West Freeway Church of Christ.
"He was wonderful", his daughter said.
The shooter appears to say something to the man, prompting him to point in a direction at the back of the church.
She still cannot believe someone would walk into a church and start shooting.
"There is evil in this world", he said.
But the 32-year-old was willing to forgive the gunman. "I don't think he had a lot of connections to very many people", he said.
Texas Lt. Gov. Dan Patrick, at a press conference after the shooting, praised the two volunteer security guards and credited the changes in state law. He said the Federal Bureau of Investigation is "working very hard to find a motive, to get to the bottom of what happened".