From the marriage point of view, there is no difference between a half and a full sibling as brother. A woman is eternally forbidden from marrying a half brother from the mother side, as well as a full brother. Therefore, half sisters from the mother side are included by the word ‘sisters’ in the following verse:
“Forbidden to you are your mothers, your daughters, your sisters, your father’s sisters and your mother’s sisters, your brother’s daughters and your sister’s daughters, your milk-mothers, your milk-sisters, the mothers of your wives, and the daughters of women whom you are married with. If you haven’t consummated the marriage (and divorced them) there will be no blame upon you (on marrying their daughters). It is also forbidden for you to marry the wives of your own sons and two sisters at the same time, although what is past is past. Indeed, Allah is the Forgiver, the Merciful.” (An-Nisa/ The Women 4:23)
From the inheritance point of view, there are differences between a sibling with same mother and a sibling with same father. When the subjects are only mother and father, father would take twice the share of the mother from the inheritance. Similarly, if it were for siblings with the same father and other siblings with the same mother, siblings with the father in common, would take two third of the inheritance where siblings with the same mother would take one third of it. (For the details of inheritance to siblings from the mother side, see An-Nisa 4:12)
Another difference in inheritance is that: When there are sisters and brothers from the mother side, they share the inheritance equally.
When brothers and sisters have the father in common, brother would inherit twice the share of the sister. However, the brother would inherit the same share as the sister, if they have only their mother in common.