What a fantastic question this is! (I know, I need to get out more often).
In very simplistic terms, you serve a Section 8 when the tenant has done something wrong. The most common cause is rent arrears although there are many other breaches of the tenancy agreement which can be listed as grounds to issue a Section 8.
A Section 21 is served when the landlord simply wants the tenant to vacate the property at the end of the tenancy or during a periodic tenancy. Even though a Section 21 is called a ‘Notice of Possession Order Form’, it does not mean that you are in trouble, it simply means that the landlord wants his house back at the end of the agreement. It is a legal document that protects both parties.
I cannot stress how important the correct completion of the forms and the actual timing of the issing of the notices (both section 8 and 21) are. If you make the simplest of mistakes be prepared for a judge to dismiss the matter immeditately and tell you start the whole process again. The reason behind this is that the law is the law and whilst the judge may sympathise with your case and reasons for issuing a Section 8, if your paperwork is not in order, he will have no option but to kick it out.
Whilst the internet is a wonderful tool and these forms are available online, I would urge landlords to resist the temptation to do it themselves: get the services of a professional.