As Schweinebacke has noted, there are two kind of differences: a) differences in availability of commands and environments b) differences in the default settings. Only the latter may be changed easily using options and commands.
Differences with regard to available commands and environments:
book
and report
feature the \chapter
sectioning command, while article
doesn't.
In book
and report
, \appendix
will cause \chapter
s to be typeset as "Appendix X" instead of "Chapter X". For article
, this isn't applicable.
book
and report
will start a new page for \part
s , while article
won't.
book
offers the \frontmatter
, \mainmatter
, and \backmatter
commands to control page numbering (Roman
for the front matter, arabic
elsewhere) and numbering of sectioning titles (no numbering in the front and back matter), while report
and article
don't.
book
doesn't offer the abstract
environment, while report
and article
do.
Differences with regard to default settings:
The book
class uses the twoside
class option (which means different margins and headers/footers for even and odd pages), while report
and article
use oneside
.
book
uses openright
(new parts and chapters start on "right" pages, adding a blank page before if necessary), while report
uses openany
. (Note that "right" means an odd page in twoside
mode, but any page in oneside
mode.) For article
, the distinction between openright
and openany
isn't applicable.
book
uses the headings
pagestyle for non-chapter-starting pages, while report
and article
always use plain
.
book
and report
use titlepage
(the title page and -- if applicable -- the abstract
environment will be typeset on pages of their own), while article
uses notitlepage
.
For book
and report
, the lowest-level sectioning command which is numbered and incorporated into the table of contents is \subsection
, while for article
it is \subsubsection
.
book
and report
will use the arguments of \chapter
s and \section
s for running headings (if such headings are present), while article
will use \section
s and \subsection
s.
book
and report
will number floats (figures, tables etc.), equations, and footnotes per chapter, while article
will number them continuously. Note that footnotes -- even when numbered per chapter -- do not feature a chapter prefix.
book
and report
will use \bibname
(which defaults to "Bibliography") for the heading of bibliographic references, while article
will use \refname
(which defaults to "References").
All of the above is valid for scrbook
v. scrreprt
vs. scrartcl
as well.