contiguous and adjacent
Definition of contiguous adjective from the Oxford Advanced Learner's Dictionary
(formal or technical)

touching or next to something
1.The countries are contiguous.

contiguous with/to something
2.The bruising was not contiguous to the wound.

http://www.oxfordlearnersdictionaries.com/definition/english/contiguous

Well... I first learned this word from vocabulary book at first . Can I just say "The countries are adjacent." and "The bruising was not near to the wound" instead?

Question

contiguous and adjacent
Definition of contiguous adjective from the Oxford Advanced Learner's Dictionary
(formal or technical)
 
touching or next to something
1.The countries are contiguous.
 
contiguous with/to something
2.The bruising was not contiguous to the wound.

http://www.oxfordlearnersdictionaries.com/definition/english/contiguous

Well... I first learned this word from vocabulary book at first . Can I just say "The countries are adjacent." and "The bruising was not near to the wound" instead?

Answer

Yes, you can say both of those, especially if you're wanting to be informal.  Most US speakers only use "contiguous" when speaking very formally.

Answer

1) The countries are contiguous.
The countries are adjacent.
The countries are touching (each other).
The countries are next to each other.

2) The bruising was not contiguous to/with the wound.
The bruising was not next to the wound.
The bruising was not touching the wound.
The bruising and the wound were not contiguous.
etc.