[?] How restricted pattern works?

Questions
1

As as far as I know, I can create patterns with conditions attached to them, like

f[x_Integer] := x

With this function I would expect something like this

Out:={2, 1.5}

Did Mathematica use any type-inference system? or just evaluated the condition and then apply his rules, if that’s the case, there are any difference between f[x_Integer] := x and f[x_ ? IntegerQ] := x

Thanks.

2

Those two definition are very similar, but the evaluation path is different, and there are cases when the outputs are different. One situation I have thought is when the function has the attribute HoldAll. The pattern x_Integer will not make any evaluation of x before deciding whether it has the head Integer, while the pattern x_?IntegerQ will evaluate IntegerQ[x], which can lead to a different answer:

Attributes[f] = {HoldAll};
Attributes[g] = {HoldAll};
f[x_Integer] := "whatever";
g[x_?IntegerQ] := "something";
f[1 - 1]
g[1 - 1]

or, with UpValues:

a /: IntegerQ[a] = True;
f[a]
g[a]