Well, it's more about semantics and vocabulary than anything else.
Techno is a term that was once more specific but today is more generic. Electronica, trance, eurodance, house and Hi-NRG....and most other types of dance music are often just lazily called "techno". Back in the old days...late 80s thru mid 90s...techno was more specific. But it has branched out.
So, in brief, Techno can now be considered a generic term for electronic music. Of which, there are two subcategories: Electronica and Dance Music.
I. Electronica is usually used for any electronic music that isn't a type of Dance Music. It uses synthesizers and all that...but actually is more influenced by rock than anything else. Artists include Crystal Method, Goldfrapp, Chemical Brothers.
II. Dance Music often includes all the rest. Trance, House, Eurodance, Freestyle, Hi-NRG, Progressive, Drum & Bass, Electro-House, Club, Dance Pop, etc etc etc are all types of Dance Music.
a. Trance is the form of dance music that's full of fast repeating melodies & harmonies with a very "electric" sound. Artists include: Tiesto, Armin Van Buuren, Filo & Peri, Paul Van Dyk, Kyau & Albert, Above & Beyond, ATB, George Acosta, Iio.
b. House is the more "soulful" type of dance music. The melodies and harmonies are less complicated, and the beat is no where near as fast as trance. Artists include: Amuka, Barbara Tucker, Andy Caldwell, Deepface, Inaya Day, Freemasons, Georgie Porgie, Jason Walker, Joi Cardwell, Dennis Ferrer.
c. Club & Dance Pop are the types of dance music that sound the most like pop/rock but has a dance beat. It's almost like mixing house and trance together. Artists include: Danielle Bollinger, Tony Moran, Amber, Dannii Minogue, Jacinta, Rachel Panay, Kristine W, Liquid 360, Lucas Prata, Mon A Q.
d. Freestyle is a rare type of dance music, although it was bigger in the 80s and 90s. It is almost like mixing Latin music with house. The beats are usually slower than other types of dance music, and less repetitive. Artists include Collage, Cynthia, Lisette Melendez, Rockell, Thiago Derucio, Malyssa..
e. Eurodance and Hi-NRG are more pop-sounding, but very fast, dance music. It's like mixing trance with pop music. Artists include: DJ Encore, Ian Van Dahl, Sylver, Milk Inc, Kate Ryan, Jessy, Lasgo, September.