Yes, Donald Trump's phones and computers were investigated by remote. He was, in fact, "wiretapped". A server at Trump Tower had a lot of communication with Alfa Bank, in Russia, and with Vladimir Putin during the summer and fall of 2016. Since nothing we do online is anonymous, the FBI noticed, and got a warrant to investigate. It was that simple. If Donald Trump thinks that any president would say no to such an investigation, he is delusional.
This differs from Watergate primarily because it was an actual investigation, complete with a warrant issued by the court for a wiretap. Watergate was spying and invasion of privacy. Nixon and et els were attempting to manipulate the success of a campaign and the outcome of a future election by criminal means. That's not what happened at Trump Tower. Due process was followed in the wiretapping of Trump Tower. No court gave Nixon permission to eavesdrop on the Democrats, but the court gave the FBI permission to investigate Donald Trump.
Another difference is that the investigation of the server at Trump Tower involves a foreign power. Had a Russian bank, with which Trump claimed he has no commerce, not been flagged, again and again, on his server, nothing would have seemed suspect. As it happens, Alfa Bank is also connected to Vladimir Putin. It would be negligent for the FBI to ignore such communiques. Nothing about this investigation compares to Watergate.