No, they are not the same. You can perform a one or two tailed test on the 1-sample, 2-sample or paired t-test. The concept of a 1 or 2 tailed test is based on how you specify the null hypothesis. If the Ho is that the means are equal and Ha is that the means are not equal, then you have a 2-tailed test. If Ho is that the means are greater than or equal and Ha is that the means are less than, then you have one version of a 1-tailed test.
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