Not exactly - Hardwood refers to the species of tree that the flooring is made from, for example, Oak, Maple and Ash are types of hardwood. Spruce, Pine and Larch are types of softwood. This term can be slightly misleading as hardwood is not necessarily harder or more dense than soft wood.
The terms come from the fact we refer to deciduous trees which lose their leaves annually as hardwood (these trees grow slowly and as a rule of thumb tend to be more dense) and referring to coniferous or evergreen trees which retain their foliage year round (conifers tend to grow faster than deciduous and as such are less dense).
Solid wood simply refers to the construction of the piece of flooring. You could have solid hardwood (a solid oak floor for example), or a solid softwood floor (pitch pine is a softwood floor a lot of us would have seen in Ireland).
An engineered oak floor could be referred to as an engineered hardwood floor.