Depending on the firm the recruitment policy on the entry level may vary.
Basically if you just graduated you'll be hired as a BA. If your have a 1-2 years of exp. you could apply for SBA position.
The differences in the job : very similar tasks, but more autonomy required on SBA role. Meaning that you can structure an analysis on your own, including the calculation cross check
. As SBA, you have more opportunity to get exposure to the next grade, with potential management of trainee (depending on the scope of the mission), but also more pressure
My recommandation would be to follow the naturel grade the firm is offering. Consultants firms are very rewarding if you perform well, and you can expect being fast tracked if you were hired too low compared to your actual performance. On the other hand if you are hired a bit to you high you may have to face some more pressure on your performance.
Hope this helps