Some definitions from authoritative sources:

caesura

A term sometimes used interchangeably with 'pause' to indicate a note that is held for longer than its written value. More specifically it was used in the Viennese Classical tradition ... to indicate where a singer or wind player should take a breath...; it is also used to denote the holding up of the metre, often heard in the Viennese waltz.¹

generalpause (G.P.)

An indication in orchestral scores ... that all players are silent at that point. It commonly occurs after a climactic passage, and was one of the notable innovations of the 18th-century Mannheim school of orchestral playing.²

A rest for the whole orchestra, usually unexpected.³

pause/fermata

A sign indicating that the note, chord, or rest over which it appears is to be prolonged at the performer's discretion. It is sometimes placed over a bar-line to indicate a short silence. It may also be used to indicate the end of a phrase, section or composition.⁴

[A] sign ... showing the end of a passage or indicating the prolongation of a note or rest beyond its usual value.... Sometimes it indicates that a cadenza or flourish should be performed.⁵

The note [or rest] should be prolonged beyond the normal duration its [notated] value would indicate.⁶

While there seems to be popular disagreement about whether a G.P. (without further indication) is of fixed or performer-determined length, the authoritative sources do not comment in this regard, but they are explicit that a fermata extends the length.

It's reasonable to conclude that Brahms intended a pause of exactly one measure. In both the G.P. and fermata cases, a shorter-than-notated silence would be indicated by a shorter associated rest or a caesura mark.

Sources

¹ _{The Oxford Companion to Music, ed. Alison Latham (Oxford University Press, 2003)}
² _{Ibid., 308}
³ _{The Norton/Grove Concise Encyclopedia of Music, ed. Stanley Sadie (Macmillan Press Ltd., 1994)}
⁴ _{Oxford, 937}
⁵ _{Norton/Grove, 603}
⁶ _{The Harvard Dictionary of Music, 310 (by way of Wikipedia)*}

TL;DR

• G.P. = "Be very, very quiet. Nobody else is playing here either." But says nothing about the duration of the rest, which is as notated.

• Fermata = Extend the rest beyond its notated value.

Some definitions from authoritative sources:

caesura

A term sometimes used interchangeably with 'pause' to indicate a note that is held for longer than its written value. More specifically it was used in the Viennese Classical tradition ... to indicate where a singer or wind player should take a breath...; it is also used to denote the holding up of the metre, often heard in the Viennese waltz.¹

generalpause (G.P.)

An indication in orchestral scores ... that all players are silent at that point. It commonly occurs after a climactic passage, and was one of the notable innovations of the 18th-century Mannheim school of orchestral playing.²

A rest for the whole orchestra, usually unexpected.³

In a score for an ensemble piece, "G.P." (General Pause) indicates silence for one bar or more for the entire ensemble. The marking of general pauses is relevant, as making noise should be avoided there—for instance, page turns in sheet music are avoided during general pauses, as the sound of players turning the page would be audible by the audience.⁴

pause/fermata

A sign indicating that the note, chord, or rest over which it appears is to be prolonged at the performer's discretion. It is sometimes placed over a bar-line to indicate a short silence. It may also be used to indicate the end of a phrase, section or composition.⁵

[A] sign ... showing the end of a passage or indicating the prolongation of a note or rest beyond its usual value.... Sometimes it indicates that a cadenza or flourish should be performed.⁶

The note [or rest] should be prolonged beyond the normal duration its [notated] value would indicate.⁷

Conclusion

While there seems to be popular disagreement about whether a G.P. (without further indication) is of fixed or performer-determined length, the authoritative sources do not comment in this regard, but they are explicit that a fermata extends the length.

It's reasonable to conclude that Brahms intended a pause of exactly one measure. In both the G.P. and fermata cases, a shorter-than-notated silence would be indicated by a shorter associated rest or a caesura mark.

Sources

¹ _{The Oxford Companion to Music, ed. Alison Latham (Oxford University Press, 2003)}
² _{Ibid., 308}
³ _{The Norton/Grove Concise Encyclopedia of Music, ed. Stanley Sadie (Macmillan Press Ltd., 1994)}
⁴ _{Elaine Gould's Behind Bars, pages 190 and 561 (by way of Wikipedia) ⁵ Oxford, 937
⁶ Norton/Grove, 603
⁷ The Harvard Dictionary of Music, 310 (by way of Wikipedia)*}