Llamar vs llamar a

[LearningSpanish]

According to Rae 'llamar' can be transitive or intransitive.

Transitive when it means to call, intransitive when it means to phone.

I really like to understand the grammar of the Spanish as much as I love to speak it but I'm having a bit of a mental block with this one, so how does that work?

1) If 'llamo a un taxi' (I am calling a taxi) uses the preposition 'a' to introduce the direct object 'un taxi' but it is also possible to say 'llamo un taxi' what
is the taxi, grammatically speaking, in the second example if it's not a direct object?

2) When does the preposition 'a' have to introduce direct objects that aren't people or personalized animals, countries etc? Does this only happen with certain verbs or what connection am I missing?

Thanks in advance for any enlightenment