I have never heard of the altar meaning the stage (although it can mean a raised platform).
The "altar" is used to refer to the "communion table". As a Baptist we do not typically refer to it as an altar because we do not view communion as a sacrament. But colloquially the altar refers to the communion table.
In my experience when Baptists use the word in service we are speaking figuratively to describe a spiritual act. Rather than figurative of a place to recieve the Eucharist it points to an older meaning of a place (figuratively) of sacrificing (in the sence of presenting our bodies as a living sacrifice).
This is the meaning of an "altar call". Most churches have moved away from the term, although out of ignorance as they equate it to a literal altar (we've changed words to old songs, like "Fill My Cup", to accommodate ignorance as well).
Anyway, I guess you could compare it to "going to the altar" meaning getting married. It doesn't refer to a piece of furnishing.
This is a good explanation from a Baptist perspective. Its interesting how Baptist will refer to Holy communion as a merely “spiritual act” which is a teaching of Zwingli. The spiritual/figurative language boils down to the Baptist view of Christology — the two Natures of Christ.
Here lies a big difference with historical liturgical minded churches (e. g. Catholics, Orthodox, Lutherans, high church Anglicans). Everything from the Narthex to the Nave to the Altar is sacred. We would not refer to things like vestments as just a piece of clothing or just a chalice or just a tabernacle or just a crucifix or just an altar …as if its merely just piece of furniture or accessory. These are sacred things set aside for sacred use in the Divine Service (Mass). The architecture of the building, confess something … this why church architecture is so important.
Another different. Everything externally catechizes … for example if a church uses plastic cups with saran wrap, they are teaching something about Holy communion or if they have a “praise band” upfront that capitulates to the culture it is catechizing the laity. Even when making the sign of the cross, it is teaching something, the thumb pinch together with the pointer and index finger represents the Trinity … the other two fingers pointing down represent the two natures of Christ. It also reminds us that we have been baptized into Christ and his church. Everything externally catechizes in the Church.
I have heard the marriage analogy from Baptist on other topics such as baptism.
At the ends of the day, views on Christology and doctrine are going to shape worship practices. For a Baptist everything is merely symbolic … therefore there is no need to have all this other stuff or even treat something as sacred (other than a Bible).