The mind that is real and true (the mind like clear water- the mind that knows and understands the truth of origin) as opposed to the mind that mistakes the creations of the self-centered imagination for the absolutely real and true. Likewise the teaching that is always honest, real and true in all times and places as opposed to the temporary, changeable and common worldly teachings peculiar to a specific time and place.

The A GLOSSARY OF TENRIKYO TERMS, Tenrikyo Overseas Department  publication offers many good examples of each use.

We have to be careful in our understanding of "true sincerity" verses the "sincerity" that is associated with worldly common truths. The mind of true sincerity see things clearly as they actually are  in the light of understanding the truth of origin whereas the sincere mind functions daily and commonly as the point of view of the self-centered imagination only.

We can see an example of these two uses in terms of our Model Story. The intention of God the Parent was to teach the truth of origin as known and understood by the mind like clear water quickly so that the people around Her would be the first to awaken single-heartedly and then acting as Her intermediaries in spreading that single-hearted awakening to the entire world. Unfortunately no one was able to understand Her intention and as it was necessary for Her to work tirelessly on model "services", appropriate to the time, place and maturity, to calm and purify the self-centered imagination so that it would be able to ponder the reasoning that flows from the truth of origin and awaken.  This is sometimes characterized as the change from the intended "evil swept away" to the preliminary preparation of the mind by "sweeping away evil". 

Though the first followers did not understand God the Parent's intention their "sincerity" was accepted in their efforts to perform a Service to purify their minds and make them open to the reason of heaven, the reason that flows from the truth of origin. 

For those performers of the Service certainly it is time to move from the "sincerity" that did not understand Her intention to the "true sincerity" that does.