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From the trac_ik_lib readme (here):

% The type can be one of the following: 
% Speed: returns very quickly the first solution found
% Distance: runs for the full timeout_in_secs, then returns the solution that minimizes SSE from the seed
% Manip1: runs for full timeout, returns solution that maximizes sqrt(det(J*J^T))
% Manip2: runs for full timeout, returns solution that minimizes cond(J) = |J|*|J^-1|

From the trac_ik_lib readme (here):

% The type can be one of the following: 
% Speed: returns very quickly the first solution found
% Distance: runs for the full timeout_in_secs, then returns the solution that minimizes SSE from the seed
% Manip1: runs for full timeout, returns solution that maximizes sqrt(det(J*J^T))
% Manip2: runs for full timeout, returns solution that minimizes cond(J) = |J|*|J^-1|