Not all e-bikes take the form of conventional push-bikes with an incorporated motor, such as the Cytronex bicycles which use a small battery disguised as a water bottle. Some are designed to take the appearance of low capacity motorcycles, but smaller in size and consisting of an electric motor rather than a petrol engine. For example, the Sakura e-bike incorporates a 200 W motor found on standard e-bikes, but also includes plastic cladding, front and rear lights, and a speedometer. It is styled as a modern moped, and is often mistaken for one.
We rode the Vado through the gauntlet, including some of the steepest hills in Palo Alto, and it easily handled everything we threw at it, maintaining a steady 20 miles per hour even on the most daunting of ascents. The bike also handles well on downhills and is both nimble and quick on city streets and paved trails. It’s even comfortable to ride for extended distances, which is vitally important for any bike built for urban settings.
The entire drive system is neatly incorporated into the bike's design for optimal weight distribution and the ultimate in sexy design, while users control torque and power output, which peaks at a surprisingly punchy 530W, via a cool Mission Control App that can also be programmed to a time or distance parameter to ensure there's enough power to get you home.
^ Consumer Product Safety Act, Pub. L. 107–319, December 4, 2002; codified at 15 U.S.C. 2085(b): The CPSC regulations do not differentiate between commercially manufactured low speed electric bicycles and those converted from ordinary bicycles by their owners using an aftermarket electric motor and battery kit, nor do they regulate the construction of electric-power bicycles using owner-built or sourced components.
Ontario is one of the last provinces in Canada to move toward legalizing power-assisted bicycles (PABs) for use on roads, even though they have been federally defined and completely legal in Canada since early 2001. In November 2005 "Bill 169" received royal assent allowing the Ministry of Transportation of Ontario (MTO) to place any vehicle on road. On October 4 2006 the Minister of Transportation for Ontario Donna Cansfield announced the Pilot Project allowing PABs which meet the federal standards definition for operation on road. PAB riders must follow the rules and regulations of a regular bicycles, wear an approved bicycle helmet and be at least 16 years or older. There are still a number of legal considerations for operating any bicycle in Ontario. 
"Medical Exemptions" are also a standard right in the State of Texas for motorcycles & even bicyclists. Through Texas's motorcycle helmet law (bicycle helmet laws from city ordinances), it is only required for those 21 years old or younger to wear a helmet. However, a medical exemption,  written by a certified licensed medical physician or licensed chiropractor, which exempts one from wearing a helmet, can be used for bicyclists if helmets are required.
The bicycle is also used for recreational purposes, such as bicycle touring, mountain biking, physical fitness, and play. Bicycle competition includes racing, BMX racing, track racing, criterium, roller racing, sportives and time trials. Major multi-stage professional events are the Giro d'Italia, the Tour de France, the Vuelta a España, the Tour de Pologne, and the Volta a Portugal.
An e-bike is identified as a "motor assisted cycle" (MAC) in British Columbia, which differs from electric mopeds and scooters, which are "limited-speed motorcycles." Motor assisted cycles must: have an electric motor of no more than 500 W; have fully operable pedals; not be capable of propelling the device at a speed greater than 32 km/hr [19.9 mph]. The engine must disengage when (a) the operator stops pedaling, (b) an accelerator controller is released, OR (c) a brake is applied. A driver's license, vehicle registration, and insurance are all not required. A bike helmet must be worn.
I would advocate you ride legal within the laws of your state. I would also look into some kind of liability rider or umbrella policy with your home owner’s policy, which covers your personal liability and theft. Get your bike registered; wear your helmet, eye protection, whatever is required by state law so that if an accident occurs and you are at fault, there is no legal recourse. Even if you own a 750W/20mph ebike that meets the definition of a bicycle, any at-fault cyclist may still be denied coverage by stingy insurance companies who want to support their clients. Your health insurance will usually cover your medical bills, but the costs of an expensive ebike may be lost.
On the other hand, the battery doesn’t lock into the bike, which means you can’t just leave it on your bike when you park at the bike rack. Anyone could walk by and simply remove your battery. That seems like an oversight to me, though perhaps the designers assumed that such a small battery would just be easy to take with you. And it is. My wife could probably lose this battery in her purse.