What is the difference between cross-linked bond and secondary bond in polymers?
This reference indicates that primary bonds in a polymer are the intramolecular bonds (the covalent bonds) that hold the polymer together. Cross-linking different chains of polymer together does occur through a covalent bond, such as a disulfide bond.

The secondary bonds that help to give the polymer its physical properties are intermolecular forces, such as hydrogen bonding for polymers that contain hydroxyl or primary or secondary amine groups. These secondary bonds can be disrupted by changing solvent conditions or heating, for example, which wouldn't disrupt the primary bonds. 

So, I suppose that you could say, loosely, that there are "two kinds of bonds between polymers in solid material" if you mean between the polymer chains before they have an opportunity to cross-link (by a change in pH, for example). After they cross-link, the physical properties of the bulk sample of the polymer will still be affected by secondary bonds, the intermolecular interactions, between the cross-linked chains. 

The primary bonds will be stronger and can only be affected by chemical changes, the secondary bonds (intermolecular forces) can be affected by changing the physical conditions.