Yes, there are a variety of fogging and non-fogging glues out there.
The same way that they will vary in thickness, drying time, etc really depends on the formula and chemical composition of the glue.
Example:
I use a range of Super-glues for modellers and they come in 2 choices quick-drying, or strong bonding neither will dry white nor fog clear parts.
Tamiya's super-glue seems to be lighting quick on drying, no time for postioning parts.
Tip:
Don't buy the small tubes of Super Glue rather look for the bigger bottles of Cyano-Acrylate glues(same stuff really).