Pearson:
Generally Linear relation
Assumes Linearity.
Correlation between height and weight
Sensitive to outliers.
Spearman:
increasing or decreasing relationship, but may not be linear. Monotonic.
Higher marks lead to lower ranks, but generally not linearly.
Does not assume Linearity.
It can be good for categorical variables and relationships.
Less Sensitive to outliers.
Ref: Internet sources