Debe vs. debería

Hola Gerald

Tricky one... but if you use "debería" (deber in the conditional) that is always meaning "should":

Debería cerrar la puerta -  He should close the door (that's what I think he should do)

Debería haber cerrado la puerta - He should have closed the door. (but he didn´t)   - this implies regret or criticism.

However, with deber in the present, you can have:

Debe cerrar la puerta - He must close the door (just same as debería but instead of should, it´s must, so that is what he must do)

Debe haber cerrado la puerta - He must have closed the door (...because there is no draft now,  so I think that is what he did - it implies a logical deduction)

Now, with other tenses, you have other meanings/nuances:

Debió cerrar la puerta

This could mean:

1. He had to close the door (but not used much as we'd probably say more naturally "Tuvo que cerrar...)

2. He must have closed the door (same as debe haber cerrado, inferred from evidence,  for example because I can’t feel the draft anymore).

Ha debido cerrar la puerta

Same as before but also conveying an action that is recent and still connected to the present. 

Debía cerrar la puerta

Same as before but with the nuance of ongoing action that is typical of the imperfect use.

Saludos cordiales 

¡Feliz Año Nuevo!

Inma