A Spaniard friend of mine is planning to travel to the USA. He has the vaccination certificate saying that he is fully vaccinated.
The problem is that, in Spain (and perhaps other countries) for patients who have already been infected within 6 months they are giving them a single shot, instead of the two shots for vaccines that would normally requires two. This is an official policy with certain Scientist backing since those patients what they want is to boost their already acquired immunity.
In his documents he is described as fully vaccinated having 1/1 required shots. Speaking to higher representatives in his province, they explained that this is enough for traveling within Europe, but, they are unsure about USA.
EDIT
He is planning to come in December, meaning that by that time USA border will follow the new policy that allows EU citizens to visit USA as long as they are vaccinated.