I wrote this handoutthis handout as a complement to Oppenheim and Willsky. Please take a look at Table 4.1 on page 14, reproduced below. (Click for larger image.) I wrote that table specifically to answer questions such as yours.
Note the similarities and differences among the four operations:
- "Series": periodic in time, discrete in frequency
- "Transform": aperiodic in time, continuous in frequency
- "Continuous Time": continuous in time, aperiodic in frequency
- "Discrete Time": discrete in time, periodic in frequency
I hope you find these notes helpful! Please feel free to distribute as you wish.