It is really school-specific as to what major and GE requirements are required, regardless of whether the degree title is BA or BS (or something else). Indeed, some highly STEM-focused schools like MIT and Harvey Mudd have extensive humanities, arts, and social studies requirements, while some other schools like Brown and Amherst or have none (or relatively little for Brown’s ABET-accredited engineering majors which have to have some).
At schools where both BA and BS programs in CS are offered, the difference is school-specific. For example, at Cornell and Wisconsin, the major requirements for the BA and BS programs in CS are the same, but the GE requirements differ:
https://www.cs.cornell.edu/undergrad/csmajor
http://guide.wisc.edu/undergraduate/letters-science/computer-sciences/#degreesmajorscertificatestext
However, Texas has different major requirements for BS, BA, and BSA versions of the CS major:
https://www.cs.utexas.edu/undergraduate/academics/curriculum-degree-plans/degree-plans/comparing-degrees
In other words, look carefully as the curriculum and offerings, rather than just the degree title.
Software engineering as a college major tends to closely resemble CS, but with more focus on software engineering methodology instead of CS topics (however, CS majors often do take a general overview software engineering course). You can compare the curricula are schools that offer both, such as San Jose State University and California Polytechnic State University.
Computer engineering, when offered as a separate major from CS, may have a more hardware design focus than CS. Again, you can compare the curricula at schools that offer both.