Simply put the difference between how counterpoint was employed in the 16th vs. 18th century may be best illustrated by comparing the music of the most outstanding practitioners of each period, namely Giovanni Palestrina and J. S. Bach.
You are on the right track in thinking that "sixteenth century counterpoint melody or modal based (as this answer suggests) and eighteenth century counterpoint harmony based."
Music composition students will generally take a semester of Species Counterpoint which covers the 16th century practice and then take Counterpoint which covers the 18th century the next semester.
One of the key differences is how Bach was able to employ harmonic counterpoint to evolve the canon into the fugue.
Another way to look at this might be to use cinema as an analogy. If I were making a modal film I would might be only showing you things in monochrome, while in a tonal film I would have everything in color, or a modal film may have all objects of the same proportions while a tonal film would have objects of varying proportions which create a harmonic or balance of proportions.
UPDATE: I was requested in the comments to add more technical details:
Modulation: when the music moves from one tonal center to another. This is found in harmony not modal.
Contrary motion: when melodic lines move in opposing directions, this may be found in both.
Form: compositional forms of the 16th century included masses, offertories, madrigal, motet, hymns, magnificats, litanies. While 18th century harmony had these forms: preludes, fugues, toccatas, inventions, variations, concertos, dance suites, and sinfonias to name a few.
This is not a complete list so it is advised that you do some homework and read up on each of the terms listed above.