IANAChemist, but to extend the cheesy analogies chemical bonds are like joint custody in a divorce; two atoms share one or more electrons. If it's split more or less evenly then it's called a covalent bond. If it's stacked in one atom's favor then it's called ionic. If it's kind of in a gray area in the middle then its called a polar covalent bond. [1]
Adhesion, even due to electrostatic or van Der Waal's forces, doesn't cause an electron to be shared [2].
To switch up the analogy (again, IANAC): as I understand it chemical bonds are like a couples thing; if you invite one you have to invite the other, and if you are interested in replacing a chemical bond with one of the atoms you need to first tear the couple apart. That's because chemical bonds share an electron; to share a particular electron with a new atom you need to stop sharing with the first one. (Sort of. I believe it's a lot more complicated than that, with group marriages and such.)
Adhesion is more like a friendship thing. You might hang out together, but there's no intimiate involvement. The electronic bonds are still available, so each each substance can do its normal chemical reaction thing with other atoms.
[1] https://en.wikipedia.org/wiki/Ionic_bonding
[2] Despite my previous cheesy analogy, electrostatic adhesion is the real static-cling force, not van Der Waal's. (But electrostatic adhesion isn't what makes sticky tape sticky, van Der Waals is.) The former is between entire molecules or groups of molecules, one group having a total positive charge compared to the other. van Der Waal's is pin-point attraction between local differences in molecular charge distribution, and each molecule in total might be electrically neutral. For example, a neutral water molecule has two highly-positive areas near the Hydrogen atoms and a highly-negative region away from them.