It is both. The term ballroom covers a lot of ground, It includes American style smooth, American style rhythm, International style standard, and International style Latin. So Latin dances are a subset of ballroom, and bolero is a member of the American style rhythm grouping. Bolero is a Latin dance. The origin of the dance is generally thought to be from Cuba. The international dance of Spain, also called bolero, is something completely different.
I wouldn't consider bolero to be a combination of any other dances. There is some similarity between all dances, but most dances stand on their own as unique dances. Bolero is Latin but it does not follow most of the rules of the other Latin dances, so you can't deduce what the footwork should be by saying it is the same as other Latin dances. Bolero is the only Latin dance I know that has rise and fall. (I don't know Paso Doble, so I won't comment on that one.) It is also the only Latin dance I know that doesn't have Latin motion (Cuban motion if you prefer). That doesn't mean you couldn't do it in a special step, but it is not considered a characteristic of the dance, and so you wouldn't want to do it very often.
Because of that rise and fall, the footwork is different from other Latin dances. If you download one of the bolero steps from this website you can see the footwork. You will see that when the first side step is taken, the first thing hitting the floor is the inside edge of the whole foot. The forward step after the man moves right (man's left foot) is toe heel, same as you do for other dances that have a lowering action. The other forward step for the man, after he moves left, is a forward scoot of the left foot while remaining on the floor.
Most instructors teach this with no foot rise, but some do teach foot rise in bolero. The video clip contains no foot rise. I don't really know which is correct without doing a popularity pole. For most American style dances you can look at the International style and get some resolution on what should be correct footwork, because International style is more regimented in what is considered correct and incorrect. American style dances tend to have more variations. Unfortunately there is no International style bolero. You can get some very definite opinions on this but there will be two camps. It's definitely more difficult with foot rise.
