diff --git a/stdlib/Random/src/Xoshiro.jl b/stdlib/Random/src/Xoshiro.jl
index ceb9b1b255339..01231f712e89a 100644
--- a/stdlib/Random/src/Xoshiro.jl
+++ b/stdlib/Random/src/Xoshiro.jl
@@ -122,6 +122,8 @@ rng_native_52(::TaskLocalRNG) = UInt64
 copy(rng::Union{TaskLocalRNG, Xoshiro}) = Xoshiro(getstate(rng)...)
 copy!(dst::Union{TaskLocalRNG, Xoshiro}, src::Union{TaskLocalRNG, Xoshiro}) = setstate!(dst, getstate(src))
 ==(x::Union{TaskLocalRNG, Xoshiro}, y::Union{TaskLocalRNG, Xoshiro}) = getstate(x) == getstate(y)
+# use a magic (random) number to scramble `h` so that `hash(x)` is distinct from `hash(getstate(x))`
+hash(x::Union{TaskLocalRNG, Xoshiro}, h::UInt) = hash(getstate(x), h + 0x49a62c2dda6fa9be % UInt)
 
 function seed!(rng::Union{TaskLocalRNG, Xoshiro})
     # as we get good randomness from RandomDevice, we can skip hashing
diff --git a/stdlib/Random/test/runtests.jl b/stdlib/Random/test/runtests.jl
index 94749b12123c3..eb5ae32965469 100644
--- a/stdlib/Random/test/runtests.jl
+++ b/stdlib/Random/test/runtests.jl
@@ -594,24 +594,41 @@ guardseed() do
     Random.seed!(typemax(UInt128))
 end
 
-# copy, == and hash
-let seed = rand(UInt32, 10)
-    r = MersenneTwister(seed)
-    @test r == MersenneTwister(seed) # r.vals should be all zeros
-    @test hash(r) == hash(MersenneTwister(seed))
-    s = copy(r)
-    @test s == r && s !== r
-    @test hash(s) == hash(r)
-    skip, len = rand(0:2000, 2)
-    for j=1:skip
-        rand(r)
-        rand(s)
+@testset "copy, == and hash" begin
+    for RNG = (MersenneTwister, Xoshiro)
+        seed = rand(UInt32, 10)
+        r = RNG(seed)
+        t = RNG(seed)
+        @test r == t
+        @test hash(r) == hash(t)
+        s = copy(r)
+        @test s == r == t && s !== r
+        @test hash(s) == hash(r)
+        skip, len = rand(0:2000, 2)
+        for j=1:skip
+            rand(r)
+            @test r != s
+            @test hash(r) != hash(s)
+            rand(s)
+        end
+        @test rand(r, len) == rand(s, len)
+        @test s == r
+        @test hash(s) == hash(r)
+        h = rand(UInt)
+        @test hash(s, h) == hash(r, h)
+        if RNG == Xoshiro
+            t = copy(TaskLocalRNG())
+            @test hash(t) == hash(TaskLocalRNG())
+            @test hash(t, h) == hash(TaskLocalRNG(), h)
+            x = rand()
+            @test hash(t) != hash(TaskLocalRNG())
+            @test rand(t) == x
+            @test hash(t) == hash(TaskLocalRNG())
+            copy!(TaskLocalRNG(), r)
+            @test hash(TaskLocalRNG()) == hash(r)
+            @test TaskLocalRNG() == r
+        end
     end
-    @test rand(r, len) == rand(s, len)
-    @test s == r
-    @test hash(s) == hash(r)
-    h = rand(UInt)
-    @test hash(s, h) == hash(r, h)
 end
 
 # MersenneTwister initialization with invalid values