As hokie66 said, almost all connections fall somewhere between fully fixed and fully pinned. Depending on where the critical loading occurs, the connection is modeled one way or the other.
In order to be sure of capturing the maximum moment transferred to the anchorage and foundation, the connection would be modeled as fixed.
In order to ensure capturing the maximum moments in the frame above, model it as a pinned connection.
Many times judgement, guided by experience, allows the designer to dismiss one model or the other as not being critical. Other times, one or the other may not be reasonable based on the level of fixity of the connection relative to other components; i.e., if the base plate connection is much more rigid than the members and connections of the rest of the frame, then modeling it a fixed may be a reasonable approximation, with the actual behavior only negligibly different from the model.
In bridge design the "15% rule" for concrete cap on multiple column type bridge piers (multi-column bents) was used for many years before automated frame analysis methods became common. It stated that if the stiffness of the column was less than 15% of the total stiffness of the connection node, the connection of the column to cap could be modeled as pinned. We compared results from that model to a frame analysis for a bent where the column stiffness was 22% of the total. The resulting moments were within 5%, with the column moments and cap moments both lower for the frame model.