Different names for cars and their definition

Lead Sled: Originally referred to extensively repaired/modified cars due to the use of lead as body filler and was, for the most part, an insult.
Since the introduction of man-made fillers (such as Bondo), the term has come to mean a post-war, large (full size) American car of the 40s, 50s and early 60's (generally up to (but not including) the 1965 model year).
A lead sled tends to have all extra side moldings shaved off and filled with the suspension lowered. Lead sleds are built for style, not speed. Some common lead sleds are the 1949 Mercury, 1949 Ford and the 1959 Cadillac.

Kustoms: These are modified cars from the 1950s and early 1960s done in the customizing styles of that time period.
The usage of a "k" for "kustom" rather than a "C", is said to have originated from car builder George Barris. This style generally consists of starting with a 2-door coupe, lowering the suspension, chopping down the roofline, sectioning and/or channeling the body, and removing most of the body trim, door handles, etc. Paint jobs often were high gloss, just about every color was used, and this paint job was usually topped off with flames, scallops, or Von Dutch (Kenny Howard or Dean Jeffries style pin striping.
These cars can also be referred to as Custom cars, leadsleds or Sleds. The term Kustom is generally used as a signifier that the cars was done in the 50s and early 60s style as opposed to later more modern styles.

Hot Rods: Hot rods are typically American cars with large engines modified for linear speed. Nobody knows for sure the origin of the term "hot rod." One explanation is that the term is a contraction of "hot roadster," meaning a roadster that was modified for speed. Open roadsters were the cars of choice to modify because they were light. Hot Rod may also refer to the connecting rods, cam, or pushrods inside the engine or to the exposed frame rails of such an automobile. It has also been noted that burning out the connecting rod bearings was a very common failure mode for souped up four-cylinder Fords, particularly the Model T, and "hot rod" could refer to that phenomenon. It was adopted in the 1930s or 1940s as the name of a car that had been "hopped up" by modifying the engine in various ways to achieve higher performance.

Chopping: To chop a roof the pillars and windows are cut down, lowering the overall roofline. "Chopping the top" goes back to the early days of hot rodding in an attempt to reduce the frontal profile of a car and increase its speed potential. Some racers on the dry lakes chopped the tops of their cars so severely that the windows were only a few inches tall. These were sometimes referred to as "mail slot" windows. This sort of bodywork is also popular on custom cars, kustoms, and leadsleds. Roof chopping also quickly became very popular with drag racers for much the same reasons as it did for lakes racers. The first roof chopper is considered to be Sam Barris who chopped and customised his brand new 1949 Mercury. Barris also pioneered a more advanced form, where the B-pillar is removed turning it into a pillarless hardtop in the process.
Concept cars, such as the AMX-GT, often undergo a lowering of their roofs even if the vehicles are based on production models. Automakers use the chopping technique to make their show cars look more sleek and "racy", although it would be impractical for normal use.

Channeling: To Channel a car the body is also lowered over the frame by removing the floor & refastening it higher inside the body, causing the body to rest closer to the ground without altering the suspension. The overall effect is to give the car body a more massive appearance. Each automobile would have its own engineering challenges as far as modifying the various components of the chassis. Local laws may prevent making the modifications too extreme, and safety would dictate some restraint. Channeling is also popular amongst hot rod, leadsled and minitruck enthusiasts, though the latter refer to it as a "body drop".

Sectioning: A related process to channeling a car (and one that has almost the same aim) is Sectioning. Sectioning is the act of removing a horizontal section from the body of a car, lowering the top half onto the bottom half and welding the result back together. The purpose is to reduce the overall height of the bodywork of the car. Like a roof chop, it also has the advantage of reducing a car's frontal area and reducing wind resistence. This sort of bodywork is popular on minitrucks, custom cars, kustoms, and leadsleds.

Rat Rod: A Rat Rod is a newly developed name for the original hot rod style of the early 1950's. A Rat Rod is usually a vehicle that has had many of it't non-critical parts removed. They are usually finished in primer or paints that are often period correct. They are very often a conglomeration of parts and pieces of different makes, models and after market parts. The term "rat rod" was first used by the high dollar, show cars guys to describe the low-buck, home built drivers. Don't forget the roots of the hobby (streetrods), it was the little guy in a garage on a budget (with help from his friends) that started it all. If you call them HOT RODS, TRADITIONAL RODS, STREETRODS, or RAT RODS they are here to stay and are making a showing at auto related events across the country. These cars are a form or art and expression of their owners and builders.

Custom Car: It is a phrase that became prominent in American pop culture in the 1950s, and has enjoyed special interest popularity since that time. It relates to a passenger vehicle that has been modified in either of the following two ways. First, a custom car may be altered to improve its performance, often by altering or replacing the engine and transmission. Second, a custom car may be a personal "styling" statement by the re-styler/re-builder, making the car look "unique" and unlike any car that might have been factory finished.

Muscle car is a term used to refer to a variety of high performance automobiles. The term principally refers to American, Australian and to a lesser extent South African models. It generally describes a 2-door rear wheel drive midsize car with a large, powerful V8 engine, and at an affordable price. Although opinions vary, it is generally accepted that classic muscle cars were produced in the late 1960s and early 1970s. Muscle cars were built for street use and in some cases racing. They are distinct from sports car and also from GTs, which are two-seat or 2+2 cars intended for high-speed touring/road racing. These are not generally considered muscle cars owing to their small size, relatively high cost and specialty nature. (The two-seater AMC AMX may or may not be an exception: one source queries whether it qualifies as a true muscle car or pony car, but also lists it among vehicles that fit the general interpretation of both categories. AMC was "never shy" about describing the car as "a genuine sports car" as it was relatively inexpensive).
For a definition from the muscle car era, a 2004 book refers the reader to an extract from Road Test magazine’s June 1967 issue: "Just what is a Muscle Car? Exactly what the name implies. It is a product of the American car industry adhering to the hot rodder's philosophy of taking a small car and putting a BIG engine in it [...] The Muscle Car is Charles Atlas kicking sand in the face of the 98 hp weakling." The book’s author adds that the muscle car was designed for straight-line speed, and did not have the "sophisticated chassis", "engineering integrity" or "lithe appearance" of European high-performance cars.
Opinions vary as to whether high-performance full-sized cars, compacts, and pony cars qualify as muscle cars.
Classic muscle cars are also defined by age and country of origin. The term "muscle car" did not enter common usage until after production of the vehicles had essentially ended, and American print media of the era commonly referred to them as "supercars".