I would answer this in two ways: HISTORICALLY, "house" and "techno" are two regional variations of post-disco club music that grew up more or less simultaneously.
House music is associated with Chicago in the early 1980s, and Techno with Detroit.
The most distinctive Chicago house sounds were "soulful" house, which used gospel diva samples, piano riffs, and inspirational raps over 4/4 beats, usually realized on an 808 drum machine; and "acid" house, which was a more stripped down "jacking" style of house that featured the TB-303 bassline, used as a melody instrument, to create a squelching, electronic style of dance music.
Detroit techno is associated with a specific set of suburban black DJs who were looking to fuse dance music with the avant-garde, sci-fi aesthetic of Kraftwerk and electro.
They featured complex, mechanical sounding beats programmed on more advanced drum machines (TR-909) and sequencers (Roland MC500), along with cold, dissonant synthesizers and vocoded voices.
These two ways of making music -- soulful, "deep" dance music, with pronounced aspects of blackness and femininity; and hard, "banging" electronic dance music, using synths and computers -- have given rise to endless variations.
To oversimplify vastly, it seems like "house" is the root style of dance music, with an almost classical feel to it.
It tends to stay closer to the 118-120BPM of disco and early 1980s club music, and has always been more hospitable to "acoustic" sounding samples, expressive divas, etc.
Techno, on the other hand, has tended to speed up, quickly reaching 130-140BPM, and becoming more and more psychedelic, until it spawned (in the 1990s)
the very influential style called "trance."
Go to a big dance party and and you will probably hear a descendant of one of these two styles.
(Unless, that is, you are listening to something with breakbeats or dub influences...)
musicfans.stackexchange.com/users/174/Robert Fink
House - very melodic music influenced by 80s disco and electro; house has simple beats and real voiceshouse examples here https://www.youtube.com/watch?v=Ki6wWg2o8uQ
Techno - very percussive, psychedelic, futuristic music that is usually not melodic
; techno has complex and variable beats of 4/4 and 2-step.
techno examples here
(this one is a compilation i made) https://www.youtube.com/watch?v=sRO0QWTsW2w
musicfans.stackexchange.com/users/1022/plopidrahtis
Adding to Robert's fantastic answer above, the name House music comes from the night club in Chicago where the sound really caught on - a night club called Warehouse and a DJ named Frankie Knuckles who created seamless mixes of repetitive disco loops using similar record mixing techniques as new york hip hoppers like Grand Master Flash.
Chicago DJ Jesse Saunders' song 'On and On' is often credited as 'the' first house record pressed.
There is a great history of electronic music documentary by Iara Lee called Modulations that really breaks down what sounds and styles came from what regions of the world and when, covering house, techno, trance, gabber, and jungle with interviews from the likes of Frankie Knuckles, Juan Atkins and more.
if you are interested, you can check it out here: https://vimeo.com/87206606
musicfans.stackexchange.com/users/545/Ryan
House has its stylistic origins in Chicago.
In Chicago, the black community heavily use gospel and blues as just the vernacular frame for their music.
The dances there is the jack and the juke .
Because of the history of gospel and blues, there is often a pronounced backbeat that is absent in techno.
Techno has its stylistic origins in Detroit.
In Detroit, gospel is in the background―sure―but jazz
is much more prominent.
The dance there is the jit (terbug).
In house music, it is always one-step.
Techno can be one-step or two-step or a hybrid of the two.
The variation enjoyed in techno over the number of step allows it to be more consistently percussive than house.
The role of the hat in techno is much more important in providing the basis of the rhythm more than the bass drum and the snares.
When we introduce Europe in the question, much of the popular dances there are one-steps and largely have a history that draws from disco and house.
The German interpretation of techno has been largely to treat it as a one-step with crosses of Berlin School and Dortmund School instrumentation.
Throughout Europe, house largely has a pulsing bassline on the off beat.
musicfans.stackexchange.com/users/3895/Phillip Siebold
OK, in short, and cutting a lot of corners: House is the EDM version of "black" music (soul, funk, jazz), and Techno is the EDM version of "white" music (rock).
House usually has a "swing" feel to it (also known as a "shuffle"), whereas Techno is played "straight".
musicfans.stackexchange.com/users/4653/Funkmeister72
answer is so simple.
house music contains Claps on the second beat in the measure, where in Techno, claps are non existent and the snare is very rarely put on the second beat in the measure.
musicfans.stackexchange.com/users/5735/Raphael
Both are considered pillars of electronic dance music, and probably its most known and recognized genres. They are often used interchangeably, sometimes to refer to electronic dance music in general, something techno and house fans consider an inaccuracy (to say the least). Tech-house is another popular genre, so apparently you can combine them both.  So, what's the difference?
What's the difference between house and techno?
musicfans.stackexchange.com
<genre><electronic-music><genre-characteristics><house><techno>
musicfans.stackexchange.com/questions/494
musicfans.stackexchange.com/users/70/Anton dB
House music is associated with early 1980s Chicago, and has a melodic music with a shuffle influenced by 80s disco and electro with simple beats and real voices. Techno is associated with Detroit, and is very percussive, futuristic and not usually melodic. House Music originates in Chicago and Techno Music originates in Detroit. House music is very melodic and has simple beats while Techno music is not very melodic and is very percussive. It is known that  House music is the EDM version of soul, funk and jazz music. Whereas Techno is the EDM version of Rock music. 
House Music originates in Chicago in the early 1980's and Techno music originates in Detroit House music is very melodic, is influenced by 80's disco music and has simple beats whilst Techno music is not melodic, very psychedelic, very percussive and futuristic House Music is the EDM version of soul, funk and jazz music that's why it usually has a ''swing'' feel to it. Whereas Techno music is played ''straight''' because it is the EDM version of rock music 