Create different arrays, and then determine if they are cell arrays of character vectors.

Test a cell array of character vectors.

C1 = {'Smith','Chung','Morales'; ...
      'Sanchez','Peterson','Adams'}

C1 = 2x3 cell
    {'Smith'  }    {'Chung'   }    {'Morales'}
    {'Sanchez'}    {'Peterson'}    {'Adams'  }

tf = iscellstr(C1)

tf = logical
   1

Every cell of C1 contains a character vector, so iscellstr returns 1.

Convert C1 to a string array and test it.

str = string(C1)

str = 2x3 string
    "Smith"      "Chung"       "Morales"
    "Sanchez"    "Peterson"    "Adams"  

tf = iscellstr(str)

tf = logical
   0

str is a string array, not a cell array, so iscellstr returns 0.

Test a cell array that contains elements of different data types.

X = rand(1,3);
C2 = {'red','blue',X}

C2=1×3 cell array
    {'red'}    {'blue'}    {1x3 double}

tf = iscellstr(C2)

tf = logical
   0

C2 has a cell that does not contain a character vector, so iscellstr returns 0.