Split string into n pieces (or pieces of length n)

JavaScript (ES6), 132 bytes

(s,t)=>+t?[...Array(-~(~-s.length/+t))].map((_,i)=>s.substr(i*t,t)):[...Array(s=+s)].map(_=>t.slice(p,p-=~((t.length-p-1)/s--)),p=0)

This is probably hopelessly over-engineered.

JavaScript (Firefox), 88 87 bytes

a=>b=>(s=+b?a:b,i=x=0,l=s.length,[for(c of s)if(r=s.slice(x,x+=+b||l/a+(i++<l%a)|0))r])

Call it like (...)("programming")(3) using Firefox 30+.

MATL, 46 26 21 27 29 42 bytes

jtU?jtbUe!tn2Gn>?0t(]tgbw(}ie]!2t$X{Oc''Zt

Try it Online! (Updated slightly to work with the latest version of the language)

Explanation

j           % Explicitly grab the first input as a string
t           % Duplicate
U           % Attempt to convert it to a number
?           % If the conversion to a number was successful
    j       % Explicitly grab the second input as a string
    t       % Duplicate the value
    b       % Bubble-up the first element in the stack
    U       % Convert to a number from a string
    e       % Reshape the string into a nGroup x nPerGroup matrix
    !       % Take the transpose
    t       % Duplicate the result
    n       % Number of characters in the repmat result
    2Gn     % Number of characters in the string
    >?      % If chars in repmat > chars in string
        O   % Zero
        t   % Duplicate 
        (   % Assign the last element to a null character (bug in MATL)
    ]       % End if statement
    t       % Duplicate this matrix
    g       % Convert to a logical matrix
    b       % Bubble-up the original string
    w       % Flip the top two elements
    (       % Assign the non-empty characters to the chars from the input string
}           % Else the string comes first
    i       % Explicitly grab the second input (the number)
    e       % Reshape the characters into an nPerGroup x nGroup 2D array
]           % End of if statement
!           % Take the transpose so it reads left-to-right
2           % Number literal
t           % Duplicate
$X{         % Call num2cell to convert to a cell array
Oc          % Null character
''          % Empty string
Zt          % Replace null chars with empty strings
            % Implicit display of stack contents