Well they are synonyms and the usage depends on the context, but I will tell you some uses for each to make it more clear..
- (فَحَصَ ) is when you go to a doctor and check on your health so you are making sure that you are fine
also when you check your car before traveling and make sure your car is good and nothing is broken
- (تَفَقَّدَ ) is when you are looking for something specifically, for example, check your bag you might have tissue! or your mom asks you where is your little sister? check (تَفَقَّدَ ) the kitchen she might be there
it's really a small difference but that's how we use each
sorry If my answer is not a big help