Rom 10:9-10, if used with the lost, cannot be a stand alone verse any more than John 3:16 can. It has to be prefaced with 1 Cor 15.
I'm sure you'll basically agree with this...
If we're going to get technical; 1 Cor. 15:1-5 is just as vague.
The very point of your OP is the issue of the need for clarity in each aspect of the terminology.
I used to preach at a Mission. It was always fascinating what various people believed about sin, about salvation; about the Cross; about died for; about rose again; you name it.
The actual gospel of Christ is 1 Cor. 15:1-5 in light of Romans 1:16-3:30, Romans 5; and the 1st half of Ephesians 2.
The various issues there; all of which can be presented in 5 min.
The sounder Grace assemblies do that much every service - without mention of the power of God unto salvation most will not even understand that.
Rather, the power of God unto salvation is made a given. As it had been for Paul (example, his reply to the Phillipian jailor implies Paul's awareness of this power of God unto salvation).
In fact, only its' content is different.
Its' basic principle is the same throughout the Scripture.
Exodus, for example...
Exodus 14:10 And when Pharaoh drew nigh, the children of Israel lifted up their eyes, and, behold, the Egyptians marched after them; and they were sore afraid: and the children of Israel cried out unto the LORD. 14:11 And they said unto Moses, Because there were no graves in Egypt, hast thou taken us away to die in the wilderness? wherefore hast thou dealt thus with us, to carry us forth out of Egypt? 14:12 Is not this the word that we did tell thee in Egypt, saying, Let us alone, that we may serve the Egyptians? For it had been better for us to serve the Egyptians, than that we should die in the wilderness. 14:13 And Moses said unto the people, Fear ye not, stand still, and see the salvation of the LORD, which he will shew to you to day: for the Egyptians whom ye have seen to day, ye shall see them again no more for ever. 14:14 The LORD shall fight for you, and ye shall hold your peace. 14:15 And the LORD said unto Moses, Wherefore criest thou unto me? speak unto the children of Israel, that they go forward: 14:16 But lift thou up thy rod, and stretch out thine hand over the sea, and divide it: and the children of Israel shall go on dry ground through the midst of the sea.
Some are just overly literal. As a result, they confuse a principle with content.
Which was Clete's point about that picture.
Anyway, even Paul makes it obvious in Cor. 15 that 1 Cor. 15:1-4 is based on much more than 1 Cor. 15:1-4.