THE TERM CONTINUOUS SIGNAL AND DISCRETE SIGNAL CLASSIFY THE SIGNALS ALONG THE TIME (i.e. horizontal axis) where as THE TERM ANALOG AND DIGITAL SIGNAL CLASSIFY THE SIGNAL ALONG THE AMPLITUDE (i.e vertical axis) we often confuse our-self with continuous time and analog signals. An analog signal is a signal which can take any amplitude in continuous range that is signal amplitude can take infinite values on the other hand a digital signal is one whose amplitude can take only finite numbers of values

Aamir, I have a little dufferent notion about the topic (it can not match the conventional notion). The question is about the difference between discrete and digital signals; it is not about the difference between them and analog signals. IMO the (binary) digital signal is a combination (set) of separate (one level) discrete signals; this combination can be transmitted in a parallel or series form.

From this viewpoint, the discrete signal is a special (simplified) case of the analog signal and the digital signal is a combination of such descrete signals (this corresponds to a multi digit number). Really, from other viewpoint, we can present a digital signal by many descrete levels (corresponding to a one digit number).

For my opinion, the header is not complete because "discrete" can mean "discrete in amplitude" (not amplitude continuous) or "discrete in time" (not time continuous) or both.

Yes, Lutz... above I meant "discretisation in amplitude"...

Most probably the discrete signal you refer to discrete-valued signal instead of discrete-time signals. In order to explain the difference let me give you an example of the digitization process of analog signal. First you sample the analog signal (continuous-valued continuous-time signal) in discrete time. Sampled signals (continuous-valued discrete-time signal) are quantized to the closest quantized levels. Quantized signal (discrete-valued discrete-time signal) could be called discrete-valued signal since it takes only discrete amplitudes from the quantization levels. Then each quantized levels you digitize it using 1's and 0'z. the resulting signal becomes digital signal.

Discrete is normally associated with time sampling. Digital is discrete in time and quantised in amplitude, usually using quantisation in a value in 2^N, for instance, if using 16 bits the integer values go from either 0 to 65535 or from -32768 to 32767.

Discrete signal usually refers to Discrete in time, unless stated otherwise. So, Discrete signal (in time) has values at only fixed intervals of times (say at n=0,1,2,3...).

Digital signal takes fixed values of amplitude A (say A=2,4,6,8....) but can have value at continuous values of time.

But the doubt is whether a digital signal can have more than two levels of quantisation? i.e. whether I can call a signal having say about four levels of quantisation (Eg. 0V,3V,5V,7V) as a digital signal ,assuming that the signal is already sampled to make the time axis discrete?

Yes, It can have more than two levels.

Usually, a digital signal can have M-ary levels, where M=1,2,4,8,16.... and so on i.e. in the power of 2, so that the values can be represented in bits by using combinations of binary values (0,1) only.

For four levels of quantisation, a signal can be represented using combination of (0,1) as 00, 01, 10, and 11.

OK.So a digital signal means one which is discretised both in amplitude and time and also it can have many levels of quantisation.Is that the correct way to put it?

IMO digital signal is one that is discrete only in amplitude (having many descrete levels). Discretisations in time and level are nessessary for the purposes of the digitalization only if we have an initial analog signal and need to obtain a digital one (ADC). But if we have initially a level discrete signal, it is exactly a digital signal... We only need to express it with some digital equivalent (a number of some numeric system). We need to do the dual DAC conversion as well - representing a number of some numeric system with a physical quantity level; in this case we have a digital signal in two corresponding forms - an abstract number and a real descrete quantity. So the discretis(z)ation and quantis(z)ation do not belong to this question.

so digital signal can be continuous? Thats a new information!!

there are four types of signals:

1. Continuous digital

2. Continuous Analog

3. Discrete Digital

4. Discrete Analog

Normally, we have Continuous analog/digital and Discrete digital signals. Discrete Analog is impossible to get as in reality, we cannot get changing waveform in zero second.   so, continuous and discrete defines time series and digital and analog defines magnitude series.

@Aamir Nawaz: What is "continuous analog"? I think, analog always is continuous (in time and amplitude). I think,  you forgot to discriminate between time and amplitude.

Example: SC circuits work discrete in time but continuous in amplitude.

No one answered clearly

Discrete signal = sampled in time; digital signal = sampled in time and quantised in amplitude.

Discrete time signal : the signals which sre discrete in time and may be continuous or discrete in value.

Continuous time signal: the signals which are continuous in time but may be continuous or discrete in the value.

Discrete signal : also called as discrete valued signal. These are the signals which are discrete in value i.e. they can attain only a specific number of distinct values.

Continuous signal: also called as continuous valued signal. These signals are continuous in value.

Analog signal: signals which are both continuous in time as well as value. Signals which are discrete in time but continuous in value are also analog signal. But these are not physically realisable. So practically, signals which are continous in both time and value are called as analog signal. Ideally, all continuous signals (valued) are analog signal.

Digital signal: signals which are discrete in value and may be continous or discrete in time are called as digital sognals. Hence all discrete signals (valued) are digital signals.

In my opinion, from the view of function, we can define them as follows: 

Thus, such conclusions can be drawn:

For example, an A/D converter first converts the analog signal into a discrete signal by sampling, then converts the discrete signal into the form of digital signal by quantization.

As for the difference between a discrete signal and a digital signal, it lies in that the latter is acquired with a quantizer from the former. And the quantization is a many-to-few mapping. Of course, if the range of a discrete signal is a subset of the output set of a quantizer, then the discrete signal is indeed a digital signal already.

See the term "Quantization" on wiki: Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a (countable) smaller set. Thus it is not limited to  two levels of quantisation, though two levels are mostly used.

Reference:

(Please see the links.)

https://en.wikipedia.org/wiki/Quantization_(signal_processing)

https://en.wikipedia.org/wiki/Analog_signal

https://en.wikipedia.org/wiki/Analog-to-digital_converter

https://en.wikipedia.org/wiki/Continuous_signal

https://en.wikipedia.org/wiki/Discrete-time_signal

http://www.umiacs.umd.edu/~ramani/cmsc828d_audio/Signals.pdf

https://en.wikibooks.org/wiki/Communication_Systems/Analog_vs._Digital