Between 'church' and 'synagogue', which one best describes the place where all the people of Jesus gather? None of them because each represents the idea of gathering in the respective language, even though most of us Christians today would not venture to go to a synagogue. The Gentiles frequented the synagogues in the time of Jesus and before Him.
We would prefer 'synagogue' instead of 'church' to remind the believers that, before the advent of Jesus in Judaism, the Gentiles joined the Israelites in their synagogues to worship the God of Israel (Isaiah 56:1-8).
With the advent of Jesus from the slums of Nazareth, the founders of the Christian Faith, which is the Messianic or Christian version of Judaism, that is, Judaism without the ceremonial rites, they were Israelites who also worshiped in synagogues and in their equivalents in Greek, ekklesias or churches in English (Acts 11:26). Besides, the synagogues are places where Moses was read for the instructions of the will of God to anyone. So, the churches or the synagogues must be places where people are instructed about the IMMUTABLE will of God so they can keep ALL of it (Deuteronomy 31:12).
Deuteronomy 31:11-13 ASV
(11) when all Israel is come to appear before Jehovah thy God in the place which he shall choose, thou shalt read this law before all Israel in their hearing. (12) Assemble the people, the men and the women and the little ones, and thy sojourner that is within thy gates, that they may hear, and that they may learn, and fear Jehovah your God, and observe to do all the words of this law; (13) and that their children, who have not known, may hear, and learn to fear Jehovah your God, as long as ye live in the land whither ye go over the Jordan to possess it.
Joshua 1:7 ASV
Only be strong and very courageous, to observe to do according to all the law, which Moses my servant commanded thee: turn not from it to the right hand or to the left, that thou mayest have good success whithersoever thou goest.
Deuteronomy 12:32 LITV
All the things that I command you, take heed to do them and you shall not add to it, nor take away from it.
Matthew 5:17-18 ASV
(17) Think not that I came to destroy the law or the prophets: I came not to destroy, but to fulfil. (18) For verily I say unto you, Till heaven and earth pass away, one jot or one tittle shall in no wise pass away from the law, till all things be accomplished.
Luke 16:17 ASV
But it is easier for heaven and earth to pass away, than for one tittle of the law to fall.
Acts 11:26 CLV
(26) and finding him, he led him to Antioch. Now it came that they are gathered a whole year, also, in the ecclesia, and teach a considerable throng. Besides, in Antioch first, the disciples are styled "Christians."
(13) All that are home-born shall do these things after this manner, in offering an offering made by fire, of a sweet savor unto Jehovah. (14) And if a stranger sojourn with you, or whosoever may be among you throughout your generations, and will offer an offering made by fire, of a sweet savor unto Jehovah; as ye do, so he shall do. (15) For the assembly, there shall be one statute for you, and for the stranger that sojourneth with you, a statute for ever throughout your generations: as ye are, so shall the sojourner be before Jehovah. (16) One law and one ordinance shall be for you, and for the stranger that sojourneth with you.
(8) But what saith it? The word is nigh thee, in thy mouth, and in thy heart: that is, the word of faith, which we preach: (9) because if thou shalt confess with thy mouth Jesus as Lord, and shalt believe in thy heart that God raised him from the dead, thou shalt be saved: (10) for with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. (11) For the scripture saith, Whosoever believeth on him shall not be put to shame. (12) For there is no distinction between Jew and Greek: for the same Lord is Lord of all, and is rich unto all that call upon him: (13) for, Whosoever shall call upon the name of the Lord shall be saved.
(26) For ye are all sons of God, through faith, in Christ Jesus.
(27) For as many of you as were baptized into Christ did put on Christ.
(28) There can be neither Jew nor Greek, there can be neither bond nor free, there can be no male and female; for ye all are one man in Christ Jesus.
(29) And if ye are Christ's, then are ye Abraham's seed, heirs according to promise.
Revelation 18:1-4 CLV
(4) And I hear another voice out of heaven, saying, "Come out of her, My people, lest you should be joint participants in her sins, and lest you should be getting of her calamities,
If the message is 'Come out of her, My people', it means that there are God's people in the midst of any sinful church, denomination, or assembly that blends Judaism with the teachings of men (Mark 7:7), with paganism. We must leave our sinful places of worship. 'My people" may not worship within other openly sinful congregations, as we read it in Revelation 18:4, contrarily to what they keep saying to themselves. 'My people' within Babylon are so stubborn! It tears my heart apart.
John 17:26 LEB
(26) And I made known to them your name, and will make it known, in order that the love with which you loved me may be in them, and I may be in them."
Luke 2:11 LEB
(11) that today a Savior, who is Christ the Lord, was born for you in the city of David.
Luke 1:31 LEB
(31) And behold, you will conceive in the womb and will give birth to a son, and you will call his name Jesus.
(3) Work is to be done six days, and in the seventh day shall be a sabbath of rest, a holy gathering; you shall do no work; it is a sabbath to Jehovah in all your dwellings.