推(tuī)荐(jiàn) means ‘recommend/recommendation’. To be specific, it means introduce the ideal person or items to another person or organization. For example,
Wǒ tuījiàn nǐ dú zhèběn shū
I recommend you read this book
‘I recommend you to read this book.’
建(jiàn)议(yì) means ‘advise/advice/suggest/suggestion’. To be precise, it means the speaker express his/her attitude or thoughts to the listen pertains to certain issue.
Wǒ jiànyì nǐ dú zhèběn shū
I advise you read this book
‘I advise you to read this book.’