For your Spearman test you give a significance (P-value) but for your Pearson test you give a strength (r-value). It is perfectly possible for an association to be very weak (e.g. r^2 much less than 0.5) and still very significant (e.g. P-value even lower than 0.001). Stregth is not the same as significance! If you really want to compare the results of a Pearson and Spearman test, please give us comparable numbers for each: either r and rho, or P values for both.

It is certainly possible for a Spearman association to be strong when a Pearson association is weak. That just means that the association is highly non-linear.

Given the results of a Spearman test, it is not possible to write a regression equation which predicts Y as a function of X. You could write an equation which predicts the rank of Y as a function of the rank of X, but that is presumably not what you are looking to do.