The issue is your topology, this is more than vertex count, but also requires vertex order. Pufferfish will work if vertex count is the same but no guarantees on the results. Any blending software (except voxel based blending like from Dendro, which will degrade your geometry resolution to some degree) will have this constraint. My example of the ball to the squid works because the squid was modeled from the ball, without adding verts or changing vert order.
So if you want to blend between shapes of completely different objects, then I am afraid to tell you that you are going to have to take the time and do the setup work to match your topologies. This will mean remodeling shape B starting from shape A (or A from B) or trying to wrap shape A’s verts onto Shape B to create a new shape B (the wrapping method also usually doesn’t work well unless the two geometries are relatively close in shape.
Take a look at these notes from Autodesk Maya about blending which are industry standard guidelines for this kind of work.
"With this method of shape animation, you create multiple target objects that are duplicates of the base object, then modify the vertex positions on each one of the target objects into the forms you want. For example, you can use this method for facial animation, with each target object representing a different facial expression.
If you’re using target objects that have a different number of vertices than the base object, you should turn off the Check Topology option. However, If the vertices are different and this option is off, you might see some unusual blending, such as an eye blending into the nose.
If the target and base objects have the same number of vertices but their order is different, Maya blends the shapes whether Check Topology is on or off. However, the position of the base object’s vertices will be transformed to the position of the target objects’ vertices. This change might cause the object to blend in a way you might not expect. To ensure a smooth transition between base and target, make sure the order of vertices is the same in both base and target objects."
In short, there is no magic solution, you have to do the setup work to create compatible shapes. After that, blending is easy.
Side Note: Why are your components missing icons?