Yes you are right - there are certain roles which have the same name but differ slightly. However, the general career progression on the "classical" consulting track is almost identical across the three MBB firms. Here is a structured description of the levels:
McKinsey – "Business Analyst" (BA) [or "(Junior) Fellow" in some markets like Germany)
BCG – “Associate”
Bain – “Associate Consultant” (AC)
Description: First two years out of undergraduate degree.
McKinsey – “Associate” (ASC)
BCG – “Consultant”
Bain – “Consultant”
Description: first post graduate school role (but with roughly 10–30% as direct promotes from Level I across firms).
Level II b
McKinsey – “Junior Engagement Manager” (JEM)
BCG – “Senior Consultant” / ”Acting PL”
Bain – “Case Team Leader” (CTL)
Description: third year after grad school and bridge to Project Manager role. Not a “formal” promotion at the firms, but definitely a precursor for promotion/designation.
McKinsey – “Engagement Manager” (EM)
BCG – “Project Leader” (PL)
Bain – “Manager”
Description: 3–7 years after grad school and responsible for day-to-day oversight of teams and main contact for client project leader. This is a formal promotion and a significant career turning point at either firm. Reaching Level III sort of proves full mastery of the general consulting toolkit in MBB quality, including team management and operational client management.
McKinsey – “Associate Partner” (AP) (formerly called "Associate Principal")
BCG – “Principal”
Bain – “Principal/Senior Manager”
Description: after 2–4 years as a Project Manager (Level III), signals greater focus on relationship management and commercial skills. Time is split across several teams to give content and context guidance. Partner case is built.
McKinsey – “Partner”
BCG – “Partner”
Bain – “Partner”
Description: on average 6–8 years after grad school. Highly engineered, formal promotion process involving a committee decision with broad spectrum of Partners from multiple global offices with stringent interviews and performance documentation process.
McKinsey – “Senior Partner” (formerly called "Director")
BCG – “Senior Partner”
Bain – “Senior Partner”
Description: effectively, Partners with tenure. Exact mechanics are a little vague, but generally Partners with 4+ years experience in the role with a consistent track record of client impact, commercial success, and meaningful IP development.