They are not the same.

There is no such university as London School of Business - there is only London Business School, which is one of the best business schools in the world and it is a constituent college of the University of London.

London School of Business and Finance, on the other hand, is an independent business school that collaborates with Grenoble Graduate School of Business (GGSB) and University of Wales to provide its MBA and it is far not the best business school (in comparison with LSB and many others). I did not find it in major UK rankings (like independent, times online etc) as well.