>Thank you all! Yet I cannot grasp the difference completely (rather subtle for my non-English ear), but surely I'm less confused now.

Just an opinion: indefinite article sounds rather wrong to me. "Use to remove a member object from a collection." sounds like you can use that method to remove any member from any collection, which is not the case. You can use it only on the members of THE collection you are mentioning, and no other.

I guess the phrasing with the indefinite article is there just by inertia, blindly following the style used when describing functions:

SIN( ) Function  
Returns the sine of an angle.