Because in the first case the expression is short circuited, so the second texture is never loaded. The expression A && B can only be true is A is true. If A is false then there is no point in evaluating B, because the expression will be false regardless. So in your code you have:
(BuildTexture("test2.bmp", testTexture2.TextureID)==FALSE)&&(BuildTexture("test3.bmp", testTexture1.TextureID)==FALSE)
First
(BuildTexture("test2.bmp", testTexture2.TextureID)==FALSE)
is evaluated. The BuildTexture call succeeds and returns TRUE, which is not equal to FALSE, so the first part of the expression evaluates to FALSE. Your expression now looks like:
(FALSE)&&(BuildTexture("test3.bmp", testTexture1.TextureID)==FALSE)
The expression can never be true, so the second BuildTexture call is never evaluated.
Similar rules work for A || B. If A is true then the expression is true regardless of B, so B does not need to be evaluated.
In this case your logic is wrong anyway. You are saying ''If both textures fail to load then show an error message, but if only one texture fails to load then continue as normal''. You want to use || instead of &&, so you are saying ''If either texture fails to load, or if both textures fail to load, then show an error message, otherwise continue as normal''.
Enigma