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VIBRATO adjective: a slightly tremulous effect imparted to vocal or instrumental tone for added warmth and expressiveness by slight and rapid variations in pitch.
1. a : the rapid reiteration of a musical tone or of alternating tones to produce a tremulous effect
b : vocal vibrato especially when prominent or excessive
2. a mechanical device in an organ for causing a tremulous (nervousness or shaky) effect.
Like many of the bad things in electric guitar history and technology, you might blame this pair of misnomers on Leo Fender. DeArmond introduced the “Tremolo Control,” (created for organs, not guitars) an amplitude-varying device with “increase” (depth) and “speed” (rate) in the early 1940’s. Harry DeArmond named his device correctly and musically. Since Leo Fender was more of a technician and a manufacturing-oriented guy than an inventor, he often co-opted inventor’s designs and made minimal changes to avoid having to pay patent rights. This would be one of those instances. Fender’s "vibrato" effect—which is technically a tremolo effect—started with its introduction on the 1956 Fender Vibrolux and Vibroverb model guitar amplifiers. The effect has commonly been misnamed ever since.
Like many inventions attributed to Leo Fender and Les Paul, the first guitar vibrato unit was a Rickenbacker design. Oddly, the device was electric only installed on Rickenbacker’s Vibrola Spanish guitars. A Rickenbacker collaborator, Doc Kauffman, designed the device and its purpose was to imitate the variable pitch of steel guitars (slide). Hand operated versions showed up on Rickenbacker's Capri guitars in the late 1950’s. Rickenbacker consistently called their devices “vibrato.” Bigsby made the first successful commercial vibrato unit (still called “vibrato” by that company), with the first known version showing up on guitars demonstrated in 1952. Merle Travis recalled the Bigsby company making a unit for him in “the late 40’s.”
Leo Fender’s “synchronized tremolo” appeared in 1954 on the Stratocaster. This might be the moment the musical effect of vibrato was misnamed "tremolo" as Fender described his device as the "tremolo arm." Thanks to Leo’s ignorance or business sense, as Wikipedia so aptly puts it, “electric guitarists traditionally use the terms ‘vibrato’ and ‘tremolo’ in the opposite senses to all other musicians when describing these hardware devices and the effects they produce.”
Oddly, in my 50+ year career in various aspects of music, I can’t remember any player ever calling this device a “tremolo.” “Whammy bar,” yes. “Tremolo” nope, not ever. Most of the musicians I’ve worked with both in bands, on stage, and in studios know the difference between “vibrato” and “tremolo.” Singers and horn players and classical string players, obviously, use the term in the musical sense and in the recording studio misnaming musical terms is grounds for ridicule and unemployment. I admit to having disliked the sound of amplitude modulation (tremolo) on guitar for more than 50 years. The Dwayne Eddy warble and the goofy sound of surf guitarists in the 1950’s is part of what helped me select the trumpet as my first instrument. So, if my dislike is displayed as cynicism, I’m good with that.
It turns out that the name for a guitar’s mechanical vibrato is brand/inventor dependent. If the mechanical vibrato device is a Fender or a Fender improvement/replacement (including Floyd Rose), it’s a “tremolo.” So much for original thought in the 21st century. If it’s a Bigsby, producing vibrato is done by using a mechanical “vibrato.”
Electronically, vibrato is one of the many things you can obtain with a pitch-shifter, chorus, and many moderately complex digital or less complicated but lower fidelity analog delay devices. Electronic tremolo is an insanely simple circuit and can be obtained for as little as $25. (Behringer’s Ultra Vibrato UV300, for example. Yeah, I know they call it a “vibrato,” but Behringer isn’t known for being smart, original, or musically or technically competent.) If you want an excuse to spend two or three times what the device is worth, you can buy all sorts of boutique tremolo pedals (that all do the same boring thing the same low-tech way) or learn something by building your own. Since the basic circuit is as simple as electronic circuits get, building a device probably provides infinitely more education value than the musical contribution this silly effect creates.
 http://www.vintageguitar.com/18545/dearmond-tremolo-control/ “DeArmond’s Tremolo Control did just this. It debuted in about 1946; the earliest known brochure is dated July of that year, according to historian Dan Formosa. ‘This precedes guitar/accordion amps with tremolo (the Premier/Danelectro amps date to 1947 and Gibson to 1948)… It’s most probable that the use of tremolo by guitarists would pre-date the commercially available units (otherwise, why would the manufacturers be prompted to create amps or effects units – unless it was an accordion thing),’ he notes. ‘The earliest recorded guitar tremolo I’ve come up with (so far) is Roosevelt Sykes, 1941-44.’” You can also read a lot about the history of this device at http://www.premierguitar.com/articles/19777-a-brief-history-of-tremolo.