Under 28.2.1a of RAE's Nueva Gramática de la Lengua Española Manual, we can read that modal verb phrases can be "radical or personal", on the one hand, and "epistemic, impersonal or propositional", on the other. This means that the modal verb ("deber" or "poder") can refer to some obligation or capability of the subject (in which case the modal is radical or personal) or can refer to the speaker's sense of necessity or probability (in which case the modal is epistemic, impersonal or propositional).
The examples RAE provides are:
No puedo ponerme estos pantalones porque me quedan chicos (subject's impossibility => radical or personal modal)
Luisa debe de haberse comprado un coche (speaker's sense of likelihood => epistemic, impersonal or propositional modal)
And then RAE provides an interesting example where there is ambiguity, depending on whether the modal is understood as referring to the subject's action (radical or personal modal) or to the speaker's understanding (epistemic, impersonal or propositional modal):
El ladrón no pudo entrar por la ventana.
If "poder" is interpreted as a radical or personal modal, the sentence above means: The burglar couldn't (= was unable to) get in through the window.
If "poder" is interpreted as an epistemic, impersonal or propositional modal, the sentence above means: The burglar can't have got(ten) in through the window.
Epistemic modals in the past can, but do not necessarily take "haber" to reinforce the epistemic interpretation and thus avoid any ambiguity:
a. Ella debió aceptar el dinero.
a1. Radical or personal interpretation: She had to accept the money.
a2. Epistemic, impersonal or propositional interpretation: She should have accepted the money.
If we want interpretation (a2) to be unequivocal, we can use (b):
b. Ella debió haber aceptado el dinero.
In epistemic usage with "haber", we can indistinctly use "debió" or "debería" and "pudo" or "podría". The modals can also be used in the present in this case (in the case of "deber", the present will only be used to mean probability and "de" can be added):
c. Ella debe (de) haber aceptado el dinero (unlike (a2) and (b) above, where "debió" expresses a reproach on the part of the speaker, in (c) "debe" expresses likelihood: She must have accepted the money)
