Is “bachelors degree of mathematics with a concentration in statistics” the same as a stat major and would having a concentration in stat mean you are a stat major of are you still technically considered as a math major?
A BA in math with a concentration in statistics means you are considered a math major.
But a major in math with a concentration in statistics could be the same thing, content-wise, as a statistics major at another college. It depends on the course that you’re required to take. Take a look at the course catalog to see the major requirements for the math major + concentration in statistics, and compare them to a statistics major at a couple of other colleges.
Would you say that a college with a statistics major would be a stronger fit and have a better/more-dedicated program for people pursuing jobs purely on statistics than ones who are a math major with a concentration in stats?
Probably. Not necessarily, not probably.
What you really need to pay attention to are the number and type of statistics courses offered in the statistics or mathematics department, the professors available to teach those courses, how often they are offered. Practically speaking, most colleges that offer a statistics major are probably going to have a larger number of undergraduate-level statistics courses in the department; more professors doing scholarship in statistics and applied mathematics; and more resources concentrated in the area.
However, statistics is a form of math - and the core coursework in statistics is math. It’d be relatively trivial in the long run for a math major with a concentration in statistics to get an MA in statistics post-college and do statistics work. And nowadays, many statisticians are dealing with increasingly complex models that benefit from higher-level work in mathematics. So depending on the kind of statistical work you want to do, you might benefit from more mathematics coursework!
However, it’s generally my experience that undergraduate colleges with statistics majors generally also have good math departments. The reverse isn’t always true.