df: displays the amount of disk space available on the file system containing each file name argument. If no file name is given, the space available on all currently mounted file systems is shown.
Example
$ df
Filesystem 1K-blocks Used Available Use% Mounted on
/dev/loop0 18761008 15246876 2554440 86% /
none 4 0 4 0% /sys/fs/cgroup
udev 493812 4 493808 1% /dev
tmpfs 100672 1364 99308 2% /run
none 5120 0 5120 0% /run/lock
none 503352 1764 501588 1% /run/shm
none 102400 20 102380 1% /run/user
/dev/sda3 174766076 164417964 10348112 95% /host
Free: Display RAM details in Linux machine
Example
$ free
total used free shared buffers cached
Mem: 8027952 4377300 3650652 0 103648 1630364
-/+ buffers/cache: 2643288 5384664
Swap: 15624188 608948 15015240
Where
Line 1: Indicates Memory details like total available RAM, used RAM, Shared RAM, RAM used for buffers, RAM used of caching content.
Line 2: Indicates total buffers/Cache used and free.
Line 3: Indicates total swap memory available, used swap and free swap memory size available.
So in short df is for disk and free is for RAM.
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