The three type of books mentioned above are taxonomical aids that offer information about species found in an area. However, the exact difference between them is not clear to me. Please explain.
A Flora describes plants and where they live. Floras typically include a dichotomous key for identification purposes and often times will include range maps as well. Floras are almost always designed to be simultaneously regionally constrained and regionally exhaustive/complete (i.e., includes all plants that grow in that region or at least all taxonomic divisions of specified taxa). See Example.
A manual applies much more broadly to plants, and typically instructs you on a subject (e.g., identification/differentiation of species). A manual does not need to be exhaustive and its scope is typically user defined (though often based on the scale/range of it's underlying subject). However, some have used the term manual to be more or less synonymous with Flora or otherwise similar document (e.g., see here).
A catalog is simply a listing of all species organized in some way. These are usually alphabetical (vs. taxonomically organized like a typical Flora). You will also never find a key in a catalog and will often find less phytographic detail.
See Chapter 6 in Describing Species: Practical Taxonomic Procedure for Biologists by Judith Winston for further assistance.