As two words, “every one” counts each one individually, as in “every single one” or “each one.”
As one word, “everyone” refers to the entire group of people. It refers to all of them in that one word.
In choosing one or the other, the writer should consider the message to be conveyed. The difference is subtle, the importance of the individual.
- When they reached the river, they split up, so every one of the wagons had to find its own way across.
- (“Every one” = “each individual wagon”)
- When all the people gathered on the other side with no casualties, everyone was safe.
- (“Everyone” here refers to the people as a group.)
- Because they had planned well and were led by an experienced guide, every one of their river crossings went well.
- (“Every one” = each of their river crossings)
- Unfortunately, they lost a few people to other accidents, so not everyone who left Missouri arrived in Oregon.
- (“Everyone” = all the people who left Missouri)