DIFFERENCE

tension /ˈtenʃn/ (n): 

# [countable, uncountable] tension (between A and B): a situation in which the fact that there are different needs or interests causes difficulties.

There is often a tension between the aims of the company and the wishes of the employees.

paradox /ˈpærədɒks/  /ˈpærədɑːks/ (n): 

# ​[countable] a person, thing or situation that has two opposite features and therefore seems strange.

He was a paradox - A loner who loved to chat to strangers.

It is a curious paradox that professional comedians often have unhappy personal lives. 

paradoxically /ˌpærəˈdɒksɪkli/  /ˌpærəˈdɑːksɪkli/ (adv):

# ​in a way that seems strange, impossible or unlikely because it has two opposite features or contains two opposite ideas.

Paradoxically, the less she ate, the fatter she got. 

paradoxical /ˌpærəˈdɒksɪkl/  /ˌpærəˈdɑːksɪkl/ (adj):

# ​(of a person, thing or situation) having two opposite features and therefore seeming strange.

It is paradoxical that some of the poorest people live in some of the richest areas of the country. 

otherwise 

counter-intuitive /ˌkaʊntər ɪnˈtjuːɪtɪv/ (adj):

# ​the opposite of what you would expect or what seems to be obvious.

These results seem counter-intuitive.

counter-intuitively /ˌkaʊntər ɪnˈtjuːɪtɪvli/ (adj):

# ​in a way that is the opposite of what you would expect or what seems to be obvious.