Eight gluons, what are the properties of two of them? If there are 8 gluons, and 6 of them can be represented as a color/anticolor pair (red/antiblue for example), that leaves 2 "other" gluons. How do these two gluons differ from each other? What happens when two quarks exchange one of these gluons? What happens when two quarks exchange the other of these gluons? Are these two gluons antiparticles of each other? What nonzero properties do they have?
If they are colorless, can they exist in isolation?
 A: All eight color states for gluons are equivalent in the sense they they are linearly-independent non-singlet color-anticolor states. You can pick any basis you want in this 8-dimensional color-anticolor space, and how you do it makes no physical difference.
(Why eight? Because three color states times three anticolor states minus one colorless singlet state leaves eight colorful color-anticolor states.)
So there are no “other” gluons. None of them are special in any way, just like neither the $xy$ nor $xz$ nor $yz$ plane in Euclidean space is special.
All gluons have color, so none exist in isolation. All have spin $1$, and in the conventional basis all are their own antiparticle.
A: An analogy: you can view the $W^3$ of $SU(2)$ as the counterpart of the "2 other gluons" of $SU(3)$.
The weak $SU(2)$ has 3 "gluons":
$$
W^1, W^2, W^3.
$$
As @G. Smith pointed out in the other answer, they are "equivalent" in the sense of Lie algebra.
However, when you pick out a specific direction (representation) to define the iso-spin up and down states $|\pm>$, say
$$
W^3 |\pm> = \pm |\pm>,
$$
then there is a diffidence between the 3 gluons: $W^1$ and $W^2$ (or their combinations $W^+$ and $W^-$) can flip the "color" (iso-spin), while $W^3$ will not change the "color" (iso-spin). Therefore, you can make an analogy between the $W^3$ of $SU(2)$ and the "2 other gluons" of $SU(3)$.
For the case of weak $SU(2)$, Mother nature took a liking to a specific iso-spin direction via the Higgs mechanism and we can tell apart an electron and a neutrino. When it comes to strong $SU(3)$, she is impartial (color blind). Any specific color assignment scheme is just a human construct.
