As I said, I never use the expression "identical particles". I only wanted to say that you find this expression in many textbooks and papers meaning "indistinguishable particles".
In quantum mechanics the particles are really indistinguishable. It's a feature you cannot intuitively understand, because it's something we are not used to in our experience with macroscopic objects which obey to a very good approximation classical laws. Macroscopic objects can be individually followed. You just mark, e.g., a ball somehow and then you can distinguish it from other similar balls by this mark. Formally you can follow its trajectory from its initial position at some time ##t_0## and identify this individual object at any later time ##t##.
This you cannot in general anymore for an individual particle in a many-body system. The many-body quantum state of indistinguishable quantities must be either symmetric or antisymmetric under exchange of two particles, describing either bosons or fermions (where the bosons have necessarily integer and fermions necessarily half-integer spin).
Take two indistinguishable particles in non-relativistic quantum mechanics. Then you can describe a pure quantum state with a two-particle wave function ##\Psi(t,\vec{x}_1,\sigma_1, \vec{x}_2,\sigma_2)##, where ##(\vec{x}_j,\sigma_j)## are positions and spin-z components (##\sigma_j \in \{\pm s,\pm (s-1),\ldots \}##). The physical meaning is, according to Born's rule, given by the two-body probability distribution
$$w(t,\vec{x}_1,\sigma_1,\vec{x}_2,\sigma_2)=|\Psi(t,\vec{x}_1,\sigma_1;\vec{x}_2,\sigma_2)|^2,$$
where
$$\mathrm{d}^3 x_1 \mathrm{d}^3 x_2 w (t,\vec{x}_1,\sigma_1,\vec{x}_2,\sigma_2)$$
is the probability to find one particle with spin component ##\sigma_1## within a volume elment ##\mathrm{d}^3 x_1## around the position ##\vec{x}_1## and one particle with spin component ##\sigma_2## within a volume element ##\mathrm{d}^3 x_2## around the position ##\vec{x}_2##.
You can only say that much about indistinguishable particles: It doesn't make sense to say you find a specific particle around ##\vec{x}_1## and another specfic particle at ##\vec{x}_2##.
Indeed from ##\Psi(t,\vec{x}_2,\sigma_2;\vec{x}_1,\sigma_1)=\pm \Psi(t,\vec{x}_1,\sigma_1;\vec{x}_2,\sigma_2)## (upper sign bosons, lower sign fermions) you get
$$w(t,\vec{x}_2,\sigma_2;\vec{x}_1,\sigma_1)=w(t,\vec{x}_1,\sigma_1;\vec{x}_2,\sigma_2),$$
i.e., it's not observable which individual particle is which.