Usage of and

And can be used in the following ways:


as a conjunction (joining two words, phrases, or clauses): Rachel plays the piano and sings.

as a way of starting a new sentence and relating it to the previous sentence:The telephone isn’t working. And that’s not the only problem.? ‘My name is Chris.’ ‘And my name is Ivan.’

1. 
   
   
   http://www.macmillandictionary.com/dictionary/british/used between http://www.macmillandictionary.com/dictionary/british/word_1, http://www.macmillandictionary.com/dictionary/british/phrase_1 etc in http://www.macmillandictionary.com/dictionary/british/order_1 to http://www.macmillandictionary.com/dictionary/british/connect them together
   
   the http://www.macmillandictionary.com/dictionary/british/lake and http://www.macmillandictionary.com/dictionary/british/mountain of Scotland
   
   Everyone was http://www.macmillandictionary.com/dictionary/british/sing_1 and http://www.macmillandictionary.com/dictionary/british/dancing.
   
   You http://www.macmillandictionary.com/dictionary/british/cook_1 the http://www.macmillandictionary.com/dictionary/british/lunch_1, and I’ll http://www.macmillandictionary.com/dictionary/british/look_1 after the http://www.macmillandictionary.com/dictionary/british/children.
   
   

This question is somewhat weird but I am confused so please help me out.

This is a definition of the word 'and' when it is used 'And' starting with a capital A, the dictionary used the word 'relating' but when 'and' is used as a conjunction like in the http://www.macmillandictionary.com/dictionary/british/lake and http://www.macmillandictionary.com/dictionary/british/mountain of Scotland, the dictionary used just the word 'connect' and then it insists that they the http://www.macmillandictionary.com/dictionary/british/lake and http://www.macmillandictionary.com/dictionary/british/mountain are not related to each other?

I know that this question is really strange but for some reason, I fell into confusion, so please share your thoughts.

Thank you so much as usual in advance.