<p>Is it possible. If so then is there any difference between a person who do so and a person who who does BS Engineering and then MS Engineering?</p>
<p>It happens, but I suggest a BS, not BA.</p>
<p>There is also “engineering physics.”</p>
<p>It’s very possible, but I’d advise contacting the engineering department and meeting with a faculty member to discuss this. Generally if you look like you would succeed in the program you have a good chance of getting in, but there may be certain courses that you could take to show interest before you get into the program. Other courses from the undergrad engineering program will be required as deficiencies as part of your M.S. program.
My wife had an M.S. in Mathematics and later finished an M.S. program in Civil/Environmental engineering. She had to take several engineering courses (IIRC she head to take statics/dynamics/mechanics/maybe engineering analysis/structural analysis/properties of materials, but she might have taken some of these out of interest or in graduate versions as part of the M.S. electives, not as required deficiencies). You might end up with an extra year of coursework due to deficiencies, which is why knocking one or more off before entering the program can be really nice.
As mentioned above, picking a branch of engineering such as Engineering Physics which has more course overlap with physics is likely to make you life easier. At least you should have all the math done.</p>