Textbooks are a good start...
I think "type" personality means trying to describe a person through dimensions of persoanlity, i.e. extroversion/introversion. There are many ways of doing this, Eyesenck proposed 3 dimensions of personality, Cartell (?) proposed like 12 (?), but modern theorists have converged on the "big five" personality dimensions.
-Limitations: does it really describe personality , surely we're more than just people on a dimensions- where do beliefs/intellect come in?
-Strengths: can predict a lot of differenent behaviour (albeit weakly)
-------------also a nomothetetic theory of personality- encompasses everything.
I THINK trait theories are when somebody creates a personality scale for ONE trait, i.e. "impulsivity", which is then used to predict a certain behaviour.
-Stregnths: can capture other things about personality that the type theories ignore, such as beliefs/political ideology.
-weaknesses: doesn't capture all aspects of personality- although it doesn't try to!