A purpose clause, as highlighted in the grammatical expression, explains why an action has taken place i.e why something happens.
e.g The boy walked to the shop (in order) to get food.
puer ad tabernam ambulavit ut cibum reciperet
In latin this is expressed with an ut + subjunctive which is either in the present tense (primary sequence) or the imperfect tense (historic sequence). For a negative purpose clause, ne + subjunctive is used instead of ut + subjunctive.
Occasionally qui is used instead of ut for a relative purpose clause.
A result clause explains the consequence/outcome of a certain action rather than why the action was performed in the first place. Like with a purpose clause, a result clause also uses ut + subjunctive for a postive result, but ut... non + subjunctive for a negative result (rather than ne + subjunctive for a purpose clause).
e.g He died SO THAT he could save his father
mortuus est ut patrem servare posset
Result clauses can often be distinguised from purpose clauses through both context and words such as tam, ita and tantus, -a, -um preceding the clause