Inverse gamma vs Pareto distribution

Question

What is the physical difference between inverse gamma and Pareto distribution. Which of them is more heavy tailed? To be precise, since both of them are heavy tailed, mean of both are defined for $\alpha>1$ and variance for $\alpha>2$. Their CDF plots also look similar. So I want to understand the difference in the applicability of these two? The cases where inverse gamma is suitable than Pareto and applications where Pareto has higher possibility to occur, then inverse gamma. Is there any difference, in the heavy tailed nature of these two, that leads to such differences