a coherent text is necessarily a cohesive text but the opposite is not true.
This is most of the time the case, but I would say not always or not exactly. The point is that coherence and cohesion are technically two different things (as Jerry also indicated). A text could be coherent (developing a central idea) but still be incohesive (lacking appropriate connections among its parts). Coherence is more abstract than cohesion. Please read the following extracts taken from Longman Dictionary of Language Teaching and Applied Linguistics
:coherence n coherent adj
A: Could you give me a lift home?
B: Sorry, I'm visiting my sister.
There's no grammatical or lexical link between A's question and B's reply (see COHESION) but the exchange has coherence because both A and B know that B's sister lives in the opposite direction to A's home.
the grammatical and/or lexical relationships between the different elements of a text.
As you see, in the example provided, there is coherence but no cohesion.