The older commercial stands were constructed with 2 boxes (like the light blue for the bottom tank on the 2nd drawing) with verticals attached on the sides with a single 3/8" bolt connecting the box to the vertical. I have one in my fish room that I purchased somewhere around 1990 that still works just fine. I have several DIY stands that I made for 10G tanks that are connected with 4 screws instead of the bolt, and I have not had any issue. Remember, for a failure to occur at that joint, the screw/bolt would have to shear (unless they weren't screwed into one of the wood members and pulled out).
I don't have the time to search the forum, but when Chriscoli moved a couple of years ago, she sold some of her old DIY stands. I bought one that holds three 4 foot tanks. on this stand, the verticals were notched to receive the horizontals that the tank sits on length wise. The joint takes the shear out, as the wood is resting on wood. There probably is a thread where she sold them that has pictures. It is more work putting them together, as you need to make a cut out the size of a 2x4 in the "edge" of another 2x4, but it reduces lumber and cost. Maybe
chriscoli
has easy access to the pictures or where she came up with the design.
Long story short, I think both of the above designs are overkill, especially for a 20 long.
One other thing to consider is the location of the verticals. On the bottom sketch, the tank needs to be slid in from the side. I build one of my stands for my 10s like this, as originally I was viewing the tank from the short end. Now that I've moved things around and have the tank oriented to view from the front, the verticals in front of the tank are a pain. You can't see in the tank, you can't remove the tank without moving the stand, and access to the tank is reduced. I would always put the verticals on the short side of the tank if you are going to view from the long side.