An implication as derived from the the previous post is that both court cases reaffirm the Constitution's commitment to preserve a sense of procedural due process to all defendants. In its interpretation of the Fourth Amendment, the court concluded that its reaches to cover those who would be considered to be the least desirable of society, namely defendants. The court's read of the concept of illegal searches and the "fruit of the poisonous tree" brings back the idea of illegal British searches of Colonial sea vessels and homes under the Writs of Assistance. The ideas that individuals should be afforded the most stringent of protection from government intrusion and that all defendants are entitled to sphere of negative freedom where they can be left alone in pursuit of a fair trial were upheld in both Weeks and Mapp cases.
Both Weeks and Mapp have to do with the "exclusionary rule." That is the legal principle that says that evidence can not be used in court against you if it has been gathered illegally.
In both Weeks and Mapp, the Supreme Court declared that evidence used against the defendants had been gathered illegally. Therefore, the evidence could not be used against them.
The difference between the two has to do with who the Supreme Court rulings applied to. In Weeks, which was decided in 1914, the trial was being held in a federal court. So that decision said that the FEDERAL government couldn't use illegally gathered evidence. However, it was still okay for STATE governments to use that kind of evidence.
In Mapp (decided in 1961) the trial was being held in STATE court so the exclusionary rule didn't apply. However, the Supreme Court decided in that case that, from then on, the exclusionary rule WOULD apply to states as well.
So -- the similarity is that they both upheld the idea of the exclusionary rule. The difference is that Weeks said it applied to the FEDERAL government while Mapp said it applied to the STATE governments too. So now it applies to both.