How many diferent "styles" (if one can call them "styles") or variations are there in Aikido?
Suppose, nobody can tell actually about that. An appropriate answer on the number of styles depends on the scale you are observing. If you aggregate styles e.g. to "style families" you will count less.
The reason for the increasing number of styles/variations: While for the first years of practice trying to copy movements of the teacher is obligatory for an Aikido student, Aikidoka practicing for a long time will recognize at one point or another, that they cannot and even must not only copy the Aikido of their teacher. They have to interpret it for themselves and for their students. A question of authenticity, very naturally, but at the same time the starting-point of a new style or variation - even if it may be rather close to the one of the teacher.
What are the main diferences between them?
- To really know a style you have to practice it profoundly, sincerely and for many years. To know the differences between styles you have to compare them and thus should really know each style you try to compare. So, how many years you need to really be able to compare let's say five styles ? Suppose more than a life.
- If somebody tries to tell about a style he/she has just watched a little bit, he/she can't tell much and that only superficially.
- Another and in my eyes very exciting way to approach an understanding of the different styles is to dive into the Aikido history including the time of Ueshiba Osensei. Osensei has developed Aikido over a long period of time and students have learned in different stages of Aikido. So you might differentiate something like "early stage Aikido", "late stage Aikido" and perhaps stages in between, referring to the timeline of Ueshiba Osensei's Aikido.
- Unfortunately there is no comprehensive history book of Aikido. At least I don't know one. And if there would be one I suspect it couldn't be complete anyway.
Hope that helps a little bit. And if you have a real question, better ask your teacher.