At UCR, Science students receive a Bachelor of Science (BSc). Social Science students, Arts & Humanities students and Interdepartmental students receive a Bachelor of Arts (BA).
These two Bachelor's degrees have their equivalent at the Master's level: Master of Arts (MA) and Master of Science (MSc). Some tracks falling under "Arts" at the bachelor's level are classified as "Science" at the graduate level, for instance Geography. Whether you can use a BA for admittance at an MSc, and the other way around, depends on the program. If you are not sure about this, look at the program's requirements listed on their website and/or contact the university directly to ask.
In addition to the MA and the MSc, there are a lot of other Master's level degrees. Examples include the Master of Business Administration (MBA), Master of Public Administration (MPA), or the Master of Music (MM).
Additionally, there is the Master of Philosophy (MPhil), which falls roughly in between a regular Master's and a doctorate degree. In the US, it is awarded to doctorate students who have completed all coursework but have not defended their dissertation. In the UK it is a degree with a program that requires two years of full-time study and a written thesis. Because it is focused on research, there is often an enhanced focus on methodology. Some students enroll in an MPhil program after already having completed another graduate program, while others enroll directly after their Bachelor's. Typically, MPhil students continue studying toward a doctorate degree after they complete their program.
There is only one degree at this level: a Doctorate of Philosophy (PhD/Ph.D/DPhil). Philosophy in this case refers to the original meaning of the word, namely "love of wisdom", not the academic discipline as we know it nowadays. People who hold this degree are referred to as a doctor (Dr.). Requirements for a PhD vary from country to country, but a doctorate program takes several years to complete pretty much everywhere.
Most students are required to do a Master's before they are admitted to a doctorate-level program, but there are exceptions. Technically, it is possible to go directly from the Bachelor's to the doctorate level. Whether it is possible for you, however, depends on your field of study and graduate university.