I'm having a real hard time understanding what the difference is between a tabular vs multidimensional model.
Don't both use dimensions and fact tables?
Can't both have a star or snowflake schema?
Don't both have measures and calculated columns?
What is the difference?
Also, if I'm using Power BI and I connect to SQL Server instead of SSAS, I can still do my thing with it. Why is SSAS needed for tabular models if you can just do it in SQL Server?
Don't both use dimensions and fact tables?
Nope. Multidimensional uses Attribute Hierarchies and Measure Groups. Tabular uses Tables, and has no built-in notion of what a "fact" or "dimension" is.
Can't both have a star or snowflake schema?
Yes. And Tabular can have other designs as well. Tabular models can have single-table, or more normalized schemas, although using a star or snowflake design is generally considered a best-practice.
Don't both have measures and calculated columns?
MD does not have calculated columns. See Comparing tabular and multidimensional solutions
Also, if I'm using Power BI and I connect to SQL Server instead of SSAS, I can still do my thing with it.
Nope. Power BI always uses a Tabular or Multi-Dimensional model. When you connect to SQL Server with Power BI you are creating a Tabular model, and either Importing the data into memory, or creating a DirectQuery model (or a hybrid). In either case there is still a Tabular Model created, either embedded in the .PBIX or in a SSAS/AAS server.