For calculating the equivalent noise bandwidth of a non-brickwall filter, I can find two different sets of numbers, both of which claim they are similar things:

Order   EqNBW
1   1.5708
2   1.1107
3   1.0472
4   1.0262
5   1.0166
6   1.0115
7   1.0084
8   1.0065
9   1.0051
10  1.0041

• RF Cafe Filter Equivalent Noise Bandwidth "Butterworth (fco = 3 dB)")
• ADC Noise Figure by Walt Kester
  • Figure 2: Relationship Between Noise Bandwidth and 3-dB Bandwidth for a Butterworth Filter
  • "will pass the same noise power as the non-ideal filter"
• Linear Circuit Design Handbook by Hank Zumbahlen
  • Figure 6-147 : "Relationship between noise bandwidth and 3 dB bandwidth for Butterworth filter"
• The Concepts of Noise Bandwidth and Cumulative Noise

1 1.57
2 1.22
3 1.16
4 1.13
5 1.12

• Equivalent Noise Bandwidth by Radio Geek
  • "have same integrated noise power"
• Equivalent Noise Bandwidth by Tim J. Sobering
  • "a noise power equivalent to the original transfer function"
• PGA309 Noise Filtering
• Operational Amplifier Noise by Art Kay
• "brick wall correction filter"

Which is correct?

Or are they both correct; just used in different calculations?