The difference between them is quite simple:
Bifidobacterium and Lactobacillus are two different bacterial genera. The term genus is used to describe a well-characterized group of organisms. As shown in the illustration, a genus is a taxonomic rank in a classification scheme used in biology and thus also for bacteria. It can be seen as a ladder: the more you go down on the ladder, the more specific information you get on the characteristics of the group.
Genus is positioned below the rank named “Family” and above “Species” on the classification ladder. Moreover, each genus has several species. Currently there are about 38 species of Bifidobacterium (e.g. Bifidobacterium bifidum) and over 128 known species of Lactobacillus (e.g. Lactobacillus acidophilus). Together they constitute a part of the intestinal microbiota in humans. You may also have heard of other genera commonly found in the human intestine, such as for example: Bacteroidetes, Clostridium, Eubacterium, Veillonella.
In case of bacteria it means that when you know the species, you know its characteristics (e.g. how does it look like, what does it eat, what does it produce) in more detail compared to when you only know the genus.