Note: Both are ‘ing’ forms of a verb, but they are different in their functions and meanings.
The Continuous Form of a Verb refers to the continuity of the action and is used as a verb only. For example:
•They are swimming in the pond. ( Here the word ‘swimming’ is in the continuous form because – 1.the word ‘swimming’ refers to the continuity of the action & 2.the word is used as a verb.)
But the Gerundial Form of a Verb refers only to the name of the action and is used as a noun. For example:
•Swimming is a good exercise. ( Here the word ‘swimming’ is in the gerundial form, not in the continuous form, because – 1.the word only refers to the name of the action, not the continuity of the action & 2. the word is used as a noun in the subject.)
Note: The gerundial form ( i.e. ‘ing’ form of a verb as noun) can be used as the subject, object or complement. For example:
•Singing is not easy. (Here ‘singing’ is in the gerundial form because it has been used as the subject.)
•I have finished writing. (Here ‘writing’ is in the gerundial form because it has been used as an object to the verb.)
•She has no interest in acting. (Here ‘acting’ is in the gerundial form because it has been used as an object to the preposition ‘in’.)
•My occupation is teaching. (Here ‘teaching’ is in the gerundial form, not in the continuous form, because it has been used as a complement. Here the word ‘teaching’ refers to the name of the profession, not to the continuity of the action as in “He is teaching his students.”)
One more important difference between Continuous Form & Gerundial Form:
Some verbs like be, belong, depend, involve, owe, like, want, love, hate, own, possesss, see, wish, appear, hear, sound, agree, disagree, promise, satisfy, believe, imagine, remember, know, understand etc. can be used in the gerundial form but not in the continuous form. For example:
•I am understanding your language. –wrong- (because it cannot be written in the continuous form. The correct form is “I understand your language.)
•I have no difficulty in understanding your language. - right- (because it can be used in the gerundial form)
•I am promising you. –wrong- (because it cannot be written in the continuous form. The correct form is “I promise you.”)
•Promising something to him is no less than a burden.-right- (because it can be written in the gerundial form.)