Connectives are used to make links between and within sentences, and they help writing to flow. 

In these sentences, things are being compared and contrasted, and the connectives used are often referred to as comparing and contrasting connectives.

Adil loves cricket. On the other hand, his brother Amir loves football.

Janey is very small. Nevertheless, she is still good at high jump.

If connectives are used to link clauses within the same sentence they are called conjunctions.

Jake likes strawberry ice cream but I prefer chocolate.

Andrew is good at maths whereas Peter is better at science.

The connectives but, yet, although, even though and whereas are all conjunctions and can be used to link clauses within a sentence. However, the following list of connectives are not conjunctions but connecting adverbs and should only be used to link separate sentences.

similarly

likewise

equally

in the same way

on the other hand

nevertheless

in contrast

however

Our tent is very old and covered in patches. However, it doesn't leak even in bad weather.

(Not: Our tent is very old and covered in patches however it doesn't leak even in bad weather.)