We present some properties recently introduced by Bal and Bhowmik: the $R$-, $H$-, and $M$-star Lindelöfness.

These properties are defined via selection principles involving the star operator and lie between covering properties (in particular, star-covering properties) and certain selective strengthenings of separability.

This dual perspective leads to several implications and connections among known properties, some of which we present.

Additionally, we provide some examples. In particular, we prove that there exists a Tychonoff M-star Lindelöf space of cardinality $\frak{c}$ which is not $R$-star Lindelöf answering a question posed by Bal and Bhowmik.