Traditionally all wood floors were solid construction, that is each board is milled from a single piece of timber to create a board. For hundreds of years sold wood floors were face fixed directly to joists to create a structural floor, that is nails were nailed through the top of the boards to the joists. Today solid floors are milled with a tongue and groove and can be secret fixed to joists so no nails are visible. Quality solid floors will be kiln dried to have moisture content suitable for use in its location (in the London and UK solid wood flooring should be kiln dried 8-10% moisture content). The key to solid floors is that they should be installed above ground and fixed to the subfloor so this rules out basements and where a floating floor is required.
The benefit of a solid floor is that its cost will be slightly cheaper than a good quality engineered floor and will last a very long time. Good quality solid wood floors will be 20-22mm thick and provide decent lengths up to 3m if Solid Oak. The down side is that board widths are limited to 180mm to avoid large gaps in the floor from expansion.
Engineered Wood Floors are very versatile, they are much more stable as layers of wood are cross bonded with the top layer being the chosen wood species. Due to engineered boards being more stable they can have much wider widths and be installed in places with higher moisture content such as basements and even bathrooms (some high end manufacturers will recommend their floors for use in bathrooms), engineered boards can also be floated on a acoustic layer so ideal for flats.
A good quality engineered board will have at least 3.5mm wear layer and lengths over 1.5m unless parquet floors are required which will have shorter fixed lengths and widths. Engineered boards can be unfinished, but more usually prefinished and with a micro bevel to avoid lipping on the edges.