For possession, relationships, illnesses and arrangements, have and have got mean exactly the same. have got is more common in spoken British English.
| Meaning | have | have got |
|---|---|---|
| Possession | They have a new car. | They've got a new car. |
| Relationships | Lisa has two brothers. | Lisa has got two brothers. |
| Illnesses | I have a headache. | I've got a headache. |
| Arrangements | I have a lesson tomorrow. | I've got a lesson tomorrow. |
In this meaning have is a state verb, so it never takes the continuous.