I am trying to add couple objects in blender and make the same distance between them without using the array modifier. Here is the picture where I want the same distance between objects. And I would also like to align the edges on the side with other objects.
Well, if you really don't want or can't use arrays, you could use a "spacer shape", of fixed width, to help you to snap adjacent objects (even if different in shapes), like this:
here I snap a third red shape keeping the same distance by snapping to the same, duplicated (or moved) blue spacer