Are there differences between SM, MS, MSc, MSci degrees?

The degree received after studying the subject at undergraduate level is often described by the field of study. For example, a BSc in mathematics would be awarded to someone who had studied mathematics at university. The same math student could obtain one of the following degrees:
Although these are all classed as "BSc", there are usually differences in the set of modules studied, and they are accepted as being at a different level. For instance, a BSc in mathematics from the Open University is regarded as equivalent to an MSci degree from other UK universities, but would not be considered as sufficient for study towards a PhD in most UK universities.
In some cases it is possible to achieve a degree in one field of study whilst studying another concurrently, for example an MSci in maths could be combined with a BSc in physics. At the same time, students are allowed to pursue multiple degrees at once by special permission of the head of department or their advisor.
Typically, for example when applying for jobs or to postgraduate study, the degree classification would be known as an MSci or MSc.
For most purposes "BSc" will suffice to indicate that one has studied science subjects at university level. For example, it is common for someone with a science BSc who has started out in research work to continue with their studies by pursuing a PhD, known as a "Doctor of Philosophy" degree.
In such cases it is typical for the research work to involve extensive study, and as such any undergraduate qualifications would be included in the PhD application. However, if their BSc was gained from studying part-time then they may need to convince the university that they have sufficient experience to pursue a PhD.
The truth is, the phrase "BSc" is simply too generic.
An MPhil (Master of Philosophy) is most often a postgraduate degree awarded by universities in many countries. The degree was originally popularized at the University of Cambridge, where it takes its name from the title of one its oldest common rooms, and is still awarded by the college of that name. The degree is typically an additional one above a PhD, and denotes particularly high research standing.
To denote the level of study, "MPhil" may be suffixed with (e.g., MSc (Econ), LLM (Law)). It may also be used to indicate the nature of the degree, with postgraduate degrees in medicine and dentistry being awarded as MMed (Medicine) and DPhil (Dentistry).
MPhil/MLitt is another name for a Master of Letters. This is an academic award at the postgraduate level conferred by universities.
This is also most often referred to as an MA (i.e., MPhil in Applied Linguistics).
A Master of Research or MRes degree is a course-based, research-focused qualification at postgraduate level in the United Kingdom and some other countries. It may be undertaken when a candidate has completed a Bachelor's degree and wishes to develop his/her knowledge and expertise in a specialist subject without going through the sometimes lengthy process of writing a doctoral dissertation.

A Master's is required when applying to some high-level positions, especially academic posts. A typical example of this is the Doctorate in Clinical Psychology (DCPsy), which is required by the UK Council for Psychotherapy for applicants to training as a psychotherapist.
In some universities, where a bachelor's degree is the normal entry requirement for master's courses, it is referred to as a 'conversion course'. In these universities it may be possible for holders of non-bachelor's degrees with substantial relevant experience to undertake such a conversion course concurrently with study towards the bachelor's degree.
The Master of Studies (MSt) is a one-year taught postgraduate degree at Oxford University, where it is a prerequisite for entrance to the DPhil in Philosophy. The MSt may also be awarded as an equivalent qualification from other colleges within the university.

A Master's by coursework or a Master of Science (MSc) is an academic degree awarded by universities in many countries.
A Master of Architecture (MArch or M.Arch.) is awarded after three to six years of post-professional study, which leads to the degree of master in architecture (M.Arch., arch.M.; architecte mba, aapmt) or master of science in architecture (M.Sc. Arch.; arch. M.Sc.).
A Master of Business Administration or MBA is an academic degree for studies in the field of business administration focusing on management with fewer general requirements, often only requiring a bachelor's degree, but varying greatly with different universities.
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The Master of Science - Professional Science (MSc - Pro Sci) is a one-year postgraduate degree at the University of Westminster. This is an interdisciplinary course which offers a practical, industry focused alternative to traditional single-discipline science and engineering MSc courses.
The Master of Applied Science (MASc) is an applied research degree offered by universities in Canada. MASc recipients undertake a long-term research project that is an expansion of their previous BSc and MSc studies into new fields or existing ones with direct applications in the professional domain. At the same time, they are able to specialize their study patterns in terms of courses and topics by combining it with further specialization in academic departments such as management, engineering, computer science, medical science and more.

source:
https://en.wikipedia.org/wiki/Master_of_Applied_Science
https://en.wikipedia.org/wiki/Master_of_Business_Administration
https://en.wikipedia.org/wiki/MSCI