Hypergeometric function particular values

Questions
1

It makes sense that

Hypergeometric2F1[a, b, b, z]

is

(1 - z)^-a

And also, it makes sense that

Hypergeometric2F1[a, -3, c, z]

is at least in most cases a polynomial (except maybe when c = -3):

(2 c + 3 c^2 + c^3 - 6 a z - 9 a c z - 3 a c^2 z + 6 a z^2 + 
 6 a^2 z^2 + 3 a c z^2 + 3 a^2 c z^2 - 2 a z^3 - 3 a^2 z^3 - 
 a^3 z^3)/(c (1 + c) (2 + c))

So, the question is then that why

Hypergeometric2F1[a, -3, -3, z]

is the polynomial

1/6 (6 + 6 a z + 3 a z^2 + 3 a^2 z^2 + 2 a z^3 + 3 a^2 z^3 + a^3 z^3)

And not (1 - z)^-a?

Obviously, the limit is different depending on which variable approaches the value. Is this well-defined based on some common knowledge or is it an arbitrary decision which value to use?

2

See here:
Complete definition:

Hypergeometric2F1[a, -n, -m, z] == 
Sum[((Pochhammer[a, k] Pochhammer[-n, k])/(Pochhammer[-m, k] k!)) z^
 k, {k, 0, n}] /; 
Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && 
 m >= n

Then for your example:

\, _2F_1(a,-3;-3;z)=\sum _{k=0}^3 \frac{\left((a)_k (-3)_k\right) z^k}{(-3)_k k!}=1+a z+\frac{1}{2} a (1+a) z^2+\frac{1}{6} a (1+a) (2+a) z^3 
 Hypergeometric2F1[a, -3, -3, z] // Expand
 (*1 + a z + (a z^2)/2 + (a^2 z^2)/2 + (a z^3)/3 + (a^2 z^3)/2 + (
  a^3 z^3)/6*)
 Sum[((Pochhammer[a, k] Pochhammer[-3, k])/(Pochhammer[-3, k] k!)) z^
     k, {k, 0, 3}] // Expand
  (*1 + a z + (a z^2)/2 + (a^2 z^2)/2 + (a z^3)/3 + (a^2 z^3)/2 + (
   a^3 z^3)/6*)

Regards M.I.