I was under the impression that freeways got the name because there was no toll.
My understanding, from the historical research I've done on the USA, the toll roads in the US were, until mid 20th century, privately made, maintained, and owned roads.
Anyway, on parkways and freeways
A parkway is a broad, landscaped highway thoroughfare. The term is particularly used for a roadway in a park or connecting to a park from which trucks and other heavy vehicles are excluded. Many parkways originally intended for scenic, recreational driving have evolved into major urban and commuter routes.
A controlled-access highway is a type of highway which has been designed for high-speed vehicular traffic, with all traffic flow and ingress/egress regulated. Common English terms are freeway (in Australia & parts of the US), motorway (in the UK and Ireland) and expressway (in Canada, parts of the US, and many Asian countries).
A controlled-access highway provides an unhindered flow of traffic, with no traffic signals, intersections or property access. They are free of any at-grade crossings with other roads, railways, or pedestrian paths, which are instead carried by overpasses and underpasses across the highway. Entrances and exits to the highway are provided at interchanges by slip roads (ramps), which allow for speed changes between the highway and arterial roads and collector roads. On the controlled-access highway, opposing directions of travel are generally separated by a median strip or central reservation containing a traffic barrier or grass. Elimination of the sources of potential conflicts with other directions of travelers dramatically improves safety, and capacity.
In the United States, a freeway is defined by the federal government's Manual on Uniform Traffic Control Devices as a divided highway with full control of access. This means two things. First, adjoining property owners do not have a legal right of access, meaning that they cannot connect their lands to the highway by constructing driveways, although frontage roads provide access to properties adjacent to a freeway in many places. When an existing road is converted into a freeway, all existing driveways must be removed and access to adjacent private lands must be blocked with fences or walls.
Second, traffic on a freeway is "free-flowing". All cross-traffic (and left-turning traffic) is relegated to overpasses or underpasses, so that there are no traffic conflicts on the main line of the highway which must be regulated by traffic lights, stop signs, or other traffic control devices. Achieving such free flow requires the construction of many overpasses, underpasses, and ramp systems. The advantage of grade-separated interchanges is that freeway drivers can almost always maintain their speed at junctions since they do not need to yield to vehicles crossing perpendicular to mainline traffic.
edit to add:
A toll road, also known as a turnpike or tollway, is a public or private roadway for which a fee (or toll) is assessed for passage. It is a form of road pricing typically implemented to help recoup the cost of road construction and maintenance, which (on public roads) amounts to a form of taxation.