Natal = Is basically a 'character analysis'
Horary = The asking of a specific question and casting a chart to glean the answer
Synastry = The comparison of two or more charts, i.e. relationship analysis
Electional = A chart cast for the most auspicious time to begin something. Often cast for wedding days, when to start a business, buy/remodel a house, ask for a loan, etc.
Financial = Most usually for those wishing to make financial investments such as in stockbroking
Medical = For health and healing issues
Vocational = To discover one's best professional/career path
Predictive = Uses progressions, solar arcs, and returns to see what's coming-up in one's life
This would be considered Synastry and Predictive
This, also, would fall under the heading of Synastry. Alas, while the entire charts of both people must be compared, with the information given it sounds like you and your daughter have a lovely compatibility.
No sighing allowed! *lol*. While astrology
is very detailed and, initially, time-consuming to learn, the rewards are so very well-worth the effort. Such knowledge is invaluable and will serve for a lifetime in assisting yourself, and your family, in steering your courses thru life to those positive outcomes you're desirous of achieving... and be of great help in those times of crises by enabling one to see the light at the end of the tunnel.
'This too shall pass' irrevocably applies to astrology as it will tell when a burden will lift. This gives hope and faith to a seeming hopelessness felt by those who do not utilize astrology's gifts.
If you wish to learn,
(as opposed to hiring an astrologer), then I would suggest taking a
professional course of study. To this end, I recommend the
AFA's,
(American Federation of Astrologers), program which can be found here:
AFA Astrology Correspondence Course http://www.astrologers.com/learn/
It's inexpensive, and the payments can be made over time. You will be assigned an astrologer as your onlilne mentor, and there is no deadline to finish the course. You go at your own pace, taking as much, or as little, time as required by you to complete the course to your satisfaction.