They are generally similar in meaning. However, 'thumping' is often associated with physical exertion: running, working out, heavy lifting, etc. On the other hand, 'pounding' is often associated with emotion: fear, excitement, physical attraction, etc.

Pumping is often referred to an irregular heart rhythm and pounding is an extra-strong heartbeat.

Thanks a lot Charlie

Thanks a lot

If the heart is pounding it means it is. Beating with an unusually strong and fast rhythm, usually because your afraid and heart thumping is fluctuations of the heart which causes irregular beats of the heart usually caused by medication or stress