Species richness is the number of different species represented in an ecological community, landscape or region. Species richness is simply a count of species, and it does not take into account the abundances of the species or their relative abundance distributions. Co-occurrence is the number of species occupying the same geographical area.

Yes, they are analogous! 

See this reference for how to represent these processes:

Spatial distribution and species co-occurrence in soil invertebrate and plant communities on northern taiga islands

Werner Ulrich, Marcin Zalewski and Alexei V. Uvarov

Annales Zoologici Fennici

Vol. 49, No. 3 (2012), pp. 161-173.

I hope this helps!

Thanks Andrew for your response. Your suggestion is helpful and insightful. However, I am looking for methods to represent co-occurrence patterns in a map, so that I correlate sp, richness and sp. co-occurrence (if this is a possibility).

Hello Daniel, there are several indices of co-occurrences, but there are more recently powerful techniques to address this issue, namely joint species distribution models. See 

http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12359/abstract

https://www.researchgate.net/publication/260838974_Understanding_co-occurrence_by_modelling_species_simultaneously_with_a_Joint_Species_Distribution_Model_JSDM?enrichId=rgreq-4db5bb56-207a-4454-aa8c-3d95f75c3d9f&enrichSource=Y292ZXJQYWdlOzI2MDgzODk3NDtBUzoxMDk2MzA3MDExODI5NzlAMTQwMzE0OTQwNTA4Nw%3D%3D&el=1_x_3

http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12514/abstract

Article Understanding co-occurrence by modelling species simultaneou...

Thanks Facundo. Your suggestions are helpful.

Species richness is the number of species present. Species co-occurrence is when the are present together. Yes, they can be depicted graphically or statistically. Examples have been presented earlier to my answer. Good luck.