Confused in difference between sequence versus signal?
In DSP we use the term signal to denote continuous-time functions as well as discrete sequences. To avoid confusion you can use the terms continuous-time signals and discrete-time signals. 

Of course, the independent variable doesn't have to be "time" (e.g., in image processing). In that case you would simply be talking about continuous or discrete signals.

Note that often you would come across the terms analog or digital signals for continuous-time and discrete-time. That categorization is a bit more ambiguous because by digital we usually mean that not only the independent variable (often "time") is discrete but also the signal values, i.e., that the signal is quantized. But in practice it's not always clear if digital is used in that strict sense. So if you don't want to restrict yourself to quantized sequences, it is advisable to use discrete(-time) instead of digital.

Take a look at this question and its answers for more details on the distinction continuous/discrete and analog/digital.