Old Time English Sequence dancing (now called Classical Sequence) is not the same as Round Dancing, but there are some similarities, as there are some similarities between most all kinds of dance. There is also Modern Sequence Dancing. One distinction between these two, is similar to one of the differences between American versus International style. Modern Sequence Dancing is done in closed position, and if you break into an open position you are doing Old Time Sequence dancing (there are some exceptions).
A large difference between round dancing and sequence dancing is that there is no cueing in sequence dancing. The dance is memorized. In round dance's beginnings, the dances were also memorized, but that is no longer done.
Note: In both sequence dancing and in round dancing, a "dance" consists of a particular song with an associated choreography. In round dance a type of dance (waltz, foxtrot, jive, etc) is called a rhythm.
I do not do sequence dancing, so my knowledge of it is not extensive, however as I understand it, a dance consists of a 16 bar pattern of steps. These steps are repeated for the duration of the song. Information about the particular dances is difficult to come by, because each of these dances is copyrighted, and it is prohibited to demonstrate, video, or copy the scripts of most of these dances without the permission of the copyright holder. That doesn't do much for promoting the popularity of this form of dance. There are many types of sequence dances, many of which would not be recognized by a ballroom dancer, such as Blues, Four Step, Gavotte, Glide, Mazurka, Party, Quadrille, Saunter, Stroll, Sway, etc. Some may recognize some of these as predecessors to some of the more modern dances. Sequence dancing also has the dances familiar to ballroom dancers, waltz, foxtrot, tango, jive, rumba, quickstep, etc.
Here is a video of sequence dancing.
http://www.youtube.com/watch?v=kDnb7Z9qKHk
Another major difference between round dance and sequence dancing is that there are competitions in sequence dancing. Competition does not exist in round dancing. Sequence dance competitions are actually pretty high level in terms of execution compared to social dancing (but you would expect that). Here is a video of a sequence dance competition.
http://www.youtube.com/watch?v=13VBQVfrDZw
Round dances (a choreography for a song) are typically split into an introduction, 2 or 3 middle parts , and an ending. The middle parts are usually repeated. All the steps are cued. Here is a page that has a video of a phase 2 dance which is the beginning level of round dance, and a phase 6 dance which is the highest level available in round dance.
http://www.crda.net/CRDAclub.html
A middle level, phase 4 may be seen here:
http://www.crda.net/
Here is a phase 6 rumba (highest level in round dance) demonstrated by a cuer and instructor.
http://www.youtube.com/watch?v=UvWCGGuMWks