What is in a name?
Nothing or a lot.
Church members are the obedient individuals in the pews who pay some money.
With the word <the baptized>, one includes all Christians.
People of God refers to a group in the Kingdom of God shouting that it wants to be heard. It is not limited to Catholics or even not to Christians.
The Lay are the uneducated people who bow the head for the insiders.
Indian Catholic Forum prefers to write on behalf of Church Citizens. They may see the Church as the city of God.
If anybody wants to organize an alternative poll for the 2023 synod, the chosen name might reveal the intention.
I would choose for VCC, votes of catholic civilians with civil or human rights as targets, the right of dissidence, and equal rights for outcasts, for women, and for LGBT people.