This is consistent with what I wrote above. There are two sounds the letters B / V make - a light B sound and a V-like sound, but not made the same way English speakers make it. But the important point is both the B and the V can make the bilabial fricitive v-like sound (and the bilabial plosive b-like sound).
I personally think it is confusing when people say “The B and the V make the same sound." While technically true, it doesn't explain that they both make the same two sounds.
According to the Diccionario panhispánico de dudas of the Real Academia Española de la Lengua (The Real Academia Española (RAE), or Spanish Royal Academy, is the institution charged with safeguarding the correct use of the Spanish language.) :
"There's no difference in the pronunciation of b and v in Spanish: both represent nowadays the bilabial voiced sound /b/. Spanish Orthography has mantained both letters, which represented different sounds in Latin, for reasons of tradition [...] The pronunciation of v as labio-dental has never existed in Spanish, and only happens occasionally in Valencian and Majorcan speakers, and in some from Southern Catalonia, when they speak Spanish, because of the influence of their regional languages, and in some places of America by influence of Amerindian languages. In every other case, it's a mistake some people make because of an excess of scrupulousness, based in recommendations from the past, for even if the Academia had recognised in its Diccionario de Autoridades (1726-1739) that "We Spaniards don't differentiate between the pronunciation of both letters", several editions of the Academia's Ortografía and Gramática in the 18th, 19th and 20th centuries described, and even recomended, the pronunciation of v as labio-dental, believing it convenient at the time to differentiate it from b as many of the great European languages, including French and English, that were then so influential, did ; but since the 1911 Gramática, the Academia ceased to explicitly recommend this differentiation. In short, the correct pronunciation of the letter v in Spanish is identical to that of b, so there's no oral difference in our language between words such as baca and vaca, bello and vello, acerbo y acervo.
As always, I also look forward to what Liss has to say!