First of all McKinsey Digital and BCG Gamma are two completely different divisions in their nature.
BCG Gamma is basically data science and advanced analytics. It will be similar to any data science job in technology. You'll be working with SQL, Python, etc. programming and analyzing data. Its career progression is closer to research than consulting. McKinsey has a similar division that is a separate entity and is called Quantum Black.
McKinsey Digital is a Former BTO. Working there has the following differences with a generalist:
1) More training - from my experience BTO guys were constantly traveling
2) Separate staffing - you will have a different staffing coordinator who has to approve all your projects. In general, it gives you more opportunities since you can also be staffed on generalist projects.
3) Different project types - BTO is working on IT strategy, Agile transformations, etc. It also depends on the country where you apply - while in US you can expect many BTO projects, in other countries most of your projects will be in various industries and functions
4) Career opportunities - again, depending on the country, the path to the partner may be easier in BTO since you have a separate group of people supporting you and dedicated projects. It may also be difficult as well if you don't have a proper BTO organization pyramid in your office
In terms of the application process - all of these divisions have separate roles from the generalist in the company websites.