Also

1-sample - compare one group to the expected result, for example, H0: The average boy's heights is 120 (H0: μ=μ0)

2-sample - compare two groups, for example, H0: The average boy's heights equal to the average girl's heights (H0: μ1=μ2)

paired t-test - compare 2 groups but dependent groups, like group1 before medicine and group2 after medicine, the same subjects.

2 tails examples, you can do the same with one tail like H0: μ>μ0 or H0: μ<μ0 or H0: μ1>μ2 or H0: μ1<μ2