What's the difference between .local, .home, and .lan?

How can I reliably address different machines on my network? I've always used the .local suffix to talk to computers on my local network before. With a new router, though, .local rarely (though sometimes) works. I've found that .home and .lan both *usually* work, but not always. .-------. .--------. .-----. | modem |---| router |))))))(wifi))))))| foo | .-------. .--------. v .-----. || | v /_^_^_\ | \))))))).-----. / cloud \ | | bar | \-_-_-/ .-----. .-----. | baz | .-----. So, from a terminal on foo, I can try: ssh bar.local ssh bar.home ssh bar.lan ssh baz.local ssh baz.home ssh baz.lan and sometimes some of those suffixes work and some don't, but I don't know how to predict which or when. foo, bar, and baz are all modern Linux or Android systems and the Linux boxes all have (or can have) avahi-daemon, or other reasonably-available packages, installed (I don't want to set up static IP addresses: I'd like to keep using DHCP (from the router) for each machine, and even if I was okay with static addresses I'd want to be able to enter hostnames in the unrooted Android machines, where I can't edit the hosts file to map a chosen hostname to an IP address.)