The main difference between L, D configuration and S, R configuration is that the first one is relative configuration while the second one is absolute configuration.

When you are distinguishing L-alanine from D-alanine, you only know that the

                                            D and L alanine - relative configuration of amine group  

group on the chiral carbon of L-alanine is on the left hand side, while in D it is on the right hand side relative in a Fischer projection. There you can't be specific about other functional groups (like or ) position.

But when you distinguish S form of Alanine from the R form, it is done by proper arrangement of the other two functional groups and a hydrogen atom. If any one of those is switched to some other position, the absolute configuration may change from S to R or from R to S. So, the configuration is more rigid in case of R-S configuration.
                                             Absolute configuration of alanine                   
As the L-D configuration doesn't specify other group's position, you can't always say S-alanine instead of L-Alanine unless you know total spatial arrangement of all functional groups of alanine.