SCR (selective catalytic reduction): SCR is the injection of ammonia into the flue gas in the presence of a catalyst to reduce NOx to nitrogen and water. It involves the installation of an SCR reactor (i.e., catalyst) at some point downstream in the process.
SNCR (selective noncatalytic reduction): SNCR is the injection of ammonia or urea into the flue gas without the use of a catalyst. The ammonia or urea is injected into specific temperature zones in the upper furnace or convective pass to reduce NOx to nitrogen and water.
The main difference is just what the names suggest: SCR is a reaction in the presence of a catalyst and SNCR does not use a catalyst. SCR is typically much more efficient at reducing NOx emissions but it is also significantly more costly because of the purchase and maintenance of the catalyst. There are also other factors that may impact the selections of one over the other, such as other constituents in the flue gas that may poison the catalyst or something as simple as having the space to install an SCR reactor.