I read that he taught many different kinds and that there are contradictions in the Nikayas on these meditation types. What are these, how many and why different types?
Vipassana and samatha is all i know that the actual Buddha taught, well in the general aspect of "actual" meditation but there are many other contemplations, like the 4 stages of death or the kasinas. Even the 4 immeasurables could be classed as meditations.
I think the real question or issue is what can be called a mediation, what is contemplation, what is a statement or factual phrase or what is intended to be experienced via meditations. for eg, Dukkha as the first noble truth is a statement "suffering exists" and then the explanation and contemplation to understand in which forms suffering exists are separate from the statement, but as to what degree do we need to meditate on Dukkha, or do we need to realize or experience it ourselves in all forms..this is the conundrum. With that trail of thought we could classify all dharmas as meditations which would leave your question as too many to count unless one has an eidetic memory and/or is a scholar who mathematically dichotomised every statement the Buddha ever said into a classification of an individual meditation.