- There are multiple ways to talk about wheel/tire sizing. "700c" is an old standard that's actually the exact same size as "622" or "29er".
- 622x14 is the ISO standard way to refer to the rim's bead seat diameter.
- 700x33 is "622x33" in ISO standard sizing. 622 means it will fit a 622 rim. 33 means that on some standard rim, the width of the inflated tire is 33mm. There's no real standard used for measuring tire width, so "same size" tires from different companies may differ by 1 or 2mm...
According to this handy chart on Sheldon Brown's website, anything from about 20-28mm width should work great on your 14mm rim.
Look for 622x20 to 622x28, or 700x20 to 700x28. You could go as large as 33mm wide, like your cross tires, but I think you'd prefer the on-road handling of tires that are more safely within the recommended range.
Whether you go more towards the high end of that range or towards the low end of that range should depend on the kind of roads you'll be riding on. If the roads are nice and smooth, 20-23mm tires may be the way to go. If there's bumps, potholes, train tracks, etc, go with 25-28mm.