I am a Windows user, so I use Putty to connect but there are similar programs for Unix.
I'm on unix and I use putty as well.
Linino = openwrt.
openwrt = Linux without GUI
Linino has quite some memory and storage.
Some differences I'm aware of (after using openwrt for 2 years)
Bash = ash
ash is similar to Bash but has less functionality. However I never found anything that didn't work for me or had an acceptable alternative.
Storage is flash so as erni says avoid writing to much. /tmp is a memory drive so you can write as much as you want there.
The SD card is auto mounted on /mnt/sda1 (yes automount works)
As you know linux is a collection of packages. Openwrt has as little packages as possible. Linino has far more packages by default and lots of room to add packages.
As to programming. You can use the toolchain that is used to build linino to make packages and install them on linino. I would call that advanced programming.
You can use any of these scripting languages to program "out of the box": php, ash, bash, lua (and probably more)
The static web site is located at /www and the dynamic web site is at /www/cgi-bin.
A word on LUA from nick gammon http://www.gammon.com.au/forum/bbshowpost.php?bbtopic_id=113
To me the most important thing is that you do not have a gui on linino and it is very likely you will add packages when stepping outside the standard arduino usage.