They are synonymous.
Well I am just going to say this I think 1 Cor 3:12-15 helps with this parable.
12 If anyone builds on this foundation using gold, silver, costly stones, wood, hay or straw, 13 their work will be shown for what it is, because the Day will bring it to light. It will be revealed with fire, and the fire will test the quality of each person’s work. 14 If what has been built survives, the builder will receive a reward. 15 If it is burned up, the builder will suffer loss but yet will be saved—even though only as one escaping through the flames.
So a person can be saved and have nothing to show for it.
In my view, (the non-Lordship Salvation view) I distinguish between justification and whether a person lives a life that pleases or disappoints God.
A person either exercises faith or they do not.
When they do, God makes the determination that they are believers/in Him, and the parable states they believed, they reached that end point.