Hmmm...I can see immediately that we need to delve into our remedial chemistry.
OK look, can you see the little bunny rabbit below?
This is a schematic of a water molecule.
The little green ears on top are each a Hydrogen atom with a positive charge at the center of each green ball.
Where the green touches the big purple ball (Oxygen) the Hydrogen, which already has only a single electron (-)
seeks a second electron, but no more than one extra. The purple ball has a total of 8 orbiting electrons, so it can easily share two of them. One spare for each green ball. Each of the green balls now have 2 electrons (one, it's own and the second from one of the 8 that the purple owns). Those electrons zip around, but spends most of their time at that interface where green meets purple. The other electrons owned by the purple are also zipping around but mostly spend their time down at the bottom part of the purple ball. The result is that the bottom of this structure has a strong negative charge but up at the top, where there are much fewer electrons, and where the protons (+) at the center of the green balls are exposed causes that general area to have a positive (+) charge. So because of that the green ears will be attracted to negatively charged particles while at the same time the bottom part of the structure will be attracted to positively charged particles. This is called a dipole and it's almost exactly the same as those little refrigerator magnets that we used to play with as kids. If you put two north poles together (or two south poles together) they repel each other, but if you reverse the orientation around, they then immediately attract each other and snap together. Well, this same behavior occurs at the the atomic level.
This is a water molecule and this behavior is why water dissolves things. It's called a dipole (two poles).
Here is a cool video describing this behavior of the electrons which makes this all possible. The pull of these poles is so strong that they can disassemble other molecules.
You can also see the potential of two water molecules being attracted to each other if the (+) green ears of one is located near the (-) purple belly of the second. This behavior on a very basic level kind of illustrates the Van der Waals force.
Here is an illustration of the process of adsorption where the target dipole molecules in a fluid are attracted to the dipole of a submerged surface molecule.

You can see the whole molecule on top does not have to be ionized. the distribution of negative and positive charges around the molecule means that some parts of the molecule will be attracted to some parts of the surface molecules. So it doesn't matter if the target molecule is broken up and ionized or not. This is an example of inter-molecular attraction and this is how activated carbon or resins such as Purigen work. They have different target molecules because the shape and charge distributions of each type of molecule is different and the substrate material itself has a specific shape and character of charge distribution. The attraction that the resin exerts must compete with the attractive forces of other charged particles in the water (such as the water molecules themselves for example), so it's not automatic that just because a particle has a charge or is ionic that it will adsorb to the surface of the resin.
Here is another schematic of activated carbon adsorption of organic molecules and it shows the pore structure (activation) which gives it a greater capacity.
TDS only addresses the quantity of things that have been dissolved by the water, which includes solids and liquids such as acids. Dissolved substances can be polar, like acids or non polar, like oils and fats. The acid will have a greater effect on conductivity (movement of electricity) than a less polar non polar materiall, but the effect on TDS will similar because it's still dissolved. So that's why there is a generic estimated conversion factor between the TDS reading and the conductivity reading, because it was determined by empirical means how much variance there is between the two measurements.
Hope this clarifies.
Cheers,