The media constantly conflates "Absentee Ballots" (which is what Trump uses) with "Vote By Mail". Despite the fact that Absentee ballots are returned via the mail, they are not at all the same thing.
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"Vote by mail" is different. It means every registered voter is mailed a ballot, whether they want one or not.
Trump's declared residence of Florida has exactly one (1) procedure for anyone who wants to vote by mail. The name Florida has given this procedure is "Vote By Mail". Any Florida resident may use this procedure for any reason they wish, including but not limited to those reasons traditionally given (in other states) for absentee balloting. It requires an application in advance in order to receive a ballot.
https://dos.myflorida.com/elections/for-voters/voting/vote-by-mail/
https://www.myfloridaelections.com/Voting-Elections/Ways-to-Vote/Vote-by-Mail-Absentee-Ballots
Typical examples are: Members of the armed forces who are away on duty, college students who are away at school, and people like Trump (and Linda and me) who own a second home that is a considerable distance from the place where they are registered to vote.
Your declared residence of Pennsylvania does have separate mail-in vs absentee ballot procedures. Both require an application in advance in order to receive a ballot. The only difference in the applications is the absentee ballot app asks for a reason, and the mail-in ballot doesn't. It's unclear why two different procedures exist, perhaps it's historical artifact.
https://www.votespa.com/Voting-in-PA/Documents/Absentee_Ballot_Application.pdf
https://www.votespa.com/Register-to-Vote/Documents/PADOS_MailInApplication.pdf
This is absolutely rife for fraud because we don't purge the rolls of registered voters, and one party in particular objects to every attempt at such a purge. That means there are lots and lots of "registered voters" in just about every jurisdiction who have died (and thus are no longer eligible to vote), or have moved away and have registered to vote elsewhere. Now let's suppose that Linda's parents (who live next door to us; we actually share a driveway) were to pass away, or move to a nursing home in another state. We would still be collecting any mail addressed to them. What would prevent us from filling out the ballots that would continue to arrive for them for years into the future in a vote-by-mail system?
There do exist a few states that are mailing out ballots without applications, I think at least some of them due to COVID-19. They are very much the exception, and it's valid to question how that's handled. I suppose you could look at Colorado, Hawaii, Oregon, Utah, and Washington to see how they've developed a strong history of free and fair elections primarily by mail. After all, whether or not you apply first, and no matter what name you call it, you do eventually get a ballot in the mail which could be stolen at that point. I'm just going to assume you know that stealing people's mail and forging their signatures is something that's actually quite difficult to get away with in a scale meaningful to most elections.
Speaking of "one party in particular", something much much easier to get away with at-scale is reshaping the set of people who are able to vote. This is done through selective purges of voter rolls just before elections rather than just after, careful selection of polling places and hours and staffing, and various other impediments to voting that statistically select against undesirable voters. When people in expensive suits with extravagant well-funded campaigns and their own television networks tell you they're worried about mail-in ballots being stolen, what they're actually worried about is mail-in ballots being cast by the intended recipient after all the time and money they spent to keep them away from the polls.