Cosplay is very broad and yes they are many different types of cosplayers so we will begin. :)
Firstly there is your usual cosplayer. A person who cosplays as a character they love and enjoy and want to do that character for self expression, pure fandom.
Then there are Crossplayers, people who cosplay as characters of the opposite sex.
This is a well known female cosplayer who goes by the name Pikmin Link, she really does pull off Link from Zelda. Her Link cosplay was that impressive Nintendo invited her to tour with them to computer game events so she could promote Nintendo products in cosplay.
This is Malro-doll another well known female cosplayer from Russia, she really pulls off James from Pokemon. As you can see not all crossplays are done for the laugh like Man Fay and can be respected. There is a very good crossplayer who has a large follow up in Belfast named Silverhairsamuari so do check her out. :)
Next up we have mecha cosplay. I find these cosplays really impressive!
Then there are Kirigumi aka Dolliers. Many people find these cosplayers frighting as they use masks instead of make up. However like furries another category kirigumi may consider themselves not cosplayers but a craft of their own. I find them very fascinating.
Furries are not the popular in the Irish con scene but seem to be very popular in the UK.*** It has questioned if furries are cosplayers or not as they wear costumes but create their own characters and have a craft of their own.
Cosplay Crossovers, this is something I would really like to try. It is when you mix cosplay with a fashion style or look eg Cosplaying as a character but wearing a steampunk outfit, cyber goth, lolita or casts, medical. These really show you are full of ideas and are creative. Like these girls cosplaying as Rei and Asuka who are mecha pilots but are wearing Elegant lolita yet they don't wear these dresses in the series.
There are also original characters in cosplay like when a person designs their own costume, look of the character and creates their own personality.
***UPDATE2017** There is a now a big furry community in Ireland. Some of them even went on Irish television.