Designing and Testing are two different phases in a 
software development process(SDLC). 
1. Information Gathering
2. Analysis
3. Designing--
4. Coding
5. Testing--
6. Implementation and Maintenance.

If u want answer in Testing terms means STLC,
designing test includes preparing Test Strategy, Test Plan 
and Test Case documents, and testing means executing the 
test cases and generating Test Reports.

Desining the application as per the requirements
Designing the application is nothing but deriving the 
functional flow , alternative flow,How many modules that we 
r handling,data flow e.tc
two types of designs are there
HLD:
In this designning team wil prepare functional architecture
i.e Functional flow
LLD: Inthis designing team will divide the total 
application into modules and theywill derive ligic for each 
module
Coding:writing the cource code as per the LLD to meet 
customer requirements

Designing means architectural design and detaile design.
Architectural design consists of data flow diagrams,flow 
charts.It is just like a blue print of the software 
application.

Detail design means unit wise design.It consists of table 
design,other database objects,screen design ,etc...

Please advise me if i am wrong.

similarly , coding means , translating the design phase 
into machine understandable language.