I read the definitions of both on wikipedia but they didn't mention any relationship between the two terms although there must be one because they are dealing with the same thing: spatial data. Can we consider that regional GISs are building blocks of a national SDI?
The way I see it is Spatial Data Infrasture is the whole network and framework of geospatial data. It involves everything from standards to data to databases to software. A desktop or web GIS can be a part of a SDI but it is not the entire SDI. All parts are required for the use and analysis of spatial data, as expressed in the following quotations:
The document which this is quoted from also gives a good indication on the different of a GIS and a SDI. See: http://www.gdmc.nl/publications/2001/Spatial_data_infrasructure.pdf
Steiniger and Hunter (2012) distinguish the following five components:
and Kuhn (2005) gives this deffintion:
Kuhn W (2005) Introduction to Spatial Data Infrastructures. Presentation held on March 14 2005. Available from: http://www.docstoc.com/docs/2697206/Introduction-to-Spatial--Data- Infrastructures
Steiniger, S. and Hunter, A.J.S. , 2012. Free and Open Source GIS Software for Building a Spatial Data Infrastructure. In: E. Bocher and M. Neteler (eds), Geospatial Free and Open Source Software in the 21st Century: Proceedings of the first Open Source Geospatial Research Symposium. Heidelberg: Springer.
ESRI 2010 - GIS Best Practices: Spatial Data Infrastructure. http://www.gdmc.nl/publications/2001/Spatial_data_infrasructure.pdf
In addition to the answer above, sometimes financial resources are also counted among the components of an SDI.