There'll Be No Distinction There comes from Blind Alfred Reed in 1929. The Carters recorded their version in 1940. Here's some info and Blind Alfred Reed's lyrics:

THERE'LL BE NO DISTINCTION THERE
(Blind Alfred Reed) (1929)

There'll be no sorrow on that heavenly shore,
There'll be no woes at the cabin door.
We'll all be wealthy and the poor will all be there,
We'll be rich and happy in that land bright and fair,
There'll be no distinction there.

There'll be no distinction there,
There'll be no distinction there,
For the Lord is just and the Lord is right,
And we'll all be white in that heavenly light,
There'll be no distinction there.

In the same kind of raiment and the same kind of shoes,
We'll all sit together in the same kind of pews,
The whites and the colored folks, the gentiles and the Jews,
We'll praise the Lord together and there'll be no drinking booze,
There'll be no distinction there.

Oh when we get to heaven, we will know and understand;
No woman will be flirting with another woman's man.
There'll be no trouble in that holy happy land;
We'll play on golden instruments and shout to beat the band,
There'll be no distinction there.

We're never blue in heaven, nothing there to wreck the mind;
Everybody is our neighbor, all the folks are good and kind.
No aggravating women there to boss the men around;
When we enter into heaven, we will wear a golden crown,
There'll be no distinction there.

This song was recorded by Blind Alfred Reed with Arville Reed in New York, NY, 3 Dec 1929 and released as RCA VICTOR Vi 23550/BLUEBIRD Bb 5882. It is related in topic to A. P. Carter's "NO DEPRESSION IN HEAVEN." THE ORIGINAL CARTER FAMILY subsequently also recorded the first two verses of Reed's song with one additional verse not to be found in Reed's version (Chicago, IL, Thursday, 3 Oct 1940; OKEH OK 05982/CONQUEROR Cq 9572). Lyrics as reprinted in liner notes for "How Can A Poor Man Stand Such Times And Live?" Rounder 1001, 1972

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THERE'LL BE NO DISTINCTION
(Carter Family 1940)

There will be no more sorrow on that heavenly shore
There'll be no wolfs a howlin' near the old cabin door
We will all be quite wealthy and there'll be no more poor
When we all get together on that heavenly shore

CHORUS: There'll be no distinction there (over there)
There'll be no distinction there
For the lord am just and the lord am right
And we'll all be white in the heavenly light
There'll be no distinction there

In the same kind of raiment in the same kind of shoes
We will all sit together in the same kind of pews
The white folks and the colored the gentile and the Jews
They will all be so happy that they doesn't refuse

They tell me up in heaven we will all be as one
And we'll all sing together when the life's crown is won
Our fathers and our mothers and sisters will be there
For they tell me up in heaven no distinction there