Differential privacy protects an individual's privacy by perturbing data on an aggregated level (DP) or individual level (LDP). We report four online human-subject experiments investigating the effects of using different approaches to communicate differential privacy techniques to laypersons in a health app data collection setting. Experiments 1 and 2 investigated participants' data disclosure decisions for low-sensitive and high-sensitive personal information when given different DP or LDP descriptions. Experiments 3 and 4 uncovered reasons behind participants' data sharing decisions, and examined participants' subjective and objective comprehensions of these DP or LDP descriptions. When shown descriptions that explain the implications instead of the definition/processes of DP or LDP technique, participants demonstrated better comprehension and showed more willingness to share information with LDP than with DP, indicating their understanding of LDP's stronger privacy guarantee compared with DP.