The wood's texture is a giveaway in terms of trying to identify the species, something I'm generally not too keen to get involved in via low resolution and poor quality images posted in places such as this. However, in this case, there is one obvious characteristic that points identification away from either an oak or a walnut in that the images show a diffuse porous wood species, i.e., a fine grained wood, candidates for which might be beech, birch, maple, etc. All the oaks are a ring porous species, (as is elm, by the way) i.e., coarse textured, with a marked difference in texture between the grain of spring and summer grown wood. Walnuts are semi-ring porous species, i.e., medium textured, and again, that characteristic isn't at all evident in the images posted.
All of which leads back to these 'walnut' and 'oak' legs being faked up, as they've been done honourably (and perhaps sometimes not so honourably) for decades or centuries, by using a cheaper white coloured or pale substitute species and polishing the result up to vaguely represent the target species through colour alone. It was common in earlier times, and still is, for example, to pass off cheaper woods such as beech, maple, etc in the form of chairs, tables, and so on as a more desirable species, such as American mahogany, all through the art of the polisher. It didn't fool anyone in the know, but the makers weren't really trying to sell to those that could tell, and it's even probable many of the buyers were/are fully aware of the deception, but didn't/don't object, ha, ha. Slainte.