Essentially they are directed at two different purposes.
Horary Astrology is used to answer questions - for example, should I start a new business? or 'Will I marry Fred/a?' It's very precise in it's focus and it's actually at the bottom of the Astrology tree - it's the sort of Astrology that you set your new apprentice on - the workaday drudgery. But it's very good for learning how to cast a chart, how to judge the strength of planets and their symbolism and how to use the houses. In the modern era, most Astrologers probably look at it with suspicion and as a leftover from a time when Astrology had magical overtones. They might also (wrongly) see it as dependent on a fatalistic view of the universe.
Electional Astrology answers questions too but a very different sort of question. It is designed to find auspicious times to perform an action. So iif my question is not 'Should I start a busines?' ' but 'When should I open the doors to my new Astrology practice?' I would turn to Electional Astrollogy.
Electional Astrology is still used by modern Astrologers, even in the West, and is at the heart of the actual practice of Jyotish in India. The aim is to pick a day and time for your 'event' which strengthens those planets that favour your undertaking and reduces the strength of those that may threaten it. A very simple example of this is that you would not want a chart in which the Lord of the eighth House is applying to an opposition to the Ascendant ruler (even if you were setting up a funeral parlour). You may well want a trine between the Ascendant ruler and the MC ruler or the MC ruler trining the Ascendant. You would also want the Ascendant ruler to have strong essential dignity, a peregrine planet or one in detriment or fall will not do. Similaarly you wouldn't want to find the Ascendant ruler in the 8th, 6th or 12th houses.
So you adjust the timing till you get the best chart you can. Note that you can never get a 'perfect' chart and you must allow for reality. If the chart says that the 'best' time for me to open the doors to my Astrology business is 2:00 AM, I will realise that that is not practically a good time. Sometimes we can't wait for the 'best' time - if the 'best' time to open my Astrology practice is in two years time, I can't wait because I need the money now.
Historically, perhaps the most famous example of an Election chart is that of John Dee, who did one for the Coronation of Elizabeth I of England. He had just a short window of opportunity because the Queen needed to be crowned and legitimised but he still needed a chart in which the significators of her enemies were weak and her own significators were strong.
Skyscript has an extract from John Frawley's 'Real Astrology' which looks at Elections
http://www.skyscript.co.uk/electional.html
Which will give you a more detailed account of the process.
Perhaps the key difference though is the scope of the reading. A horary reading is very much a hear and now limited reading. An electional reading can have repurcussions into the future for many years - My Astrology practice is not just something I'm going to do this week, I might be thinking of it as a career for the next 20 or 30 years, and the business takes on a life of it's own. Dee's Coronation chart was for a Queen who would reign for well over 40 years, with repurcussions for not just herself but the nation and indeed the international community.
