Difference between ${} and $() in Bash

I have two questions and could use some help understanding them.

1. What is the difference between ${} and $()? I understand that () means running command in separate shell and placing $ means passing the value to variable. Can someone help me in understanding this? Please correct me if I am wrong.

2. If we can use for ((i=0;i<10;i++)); do echo $i; done and it works fine then why can't I use it as while ((i=0;i<10;i++)); do echo $i; done? What is the difference in execution cycle for both?

The syntax is token-level, so the meaning of the dollar sign depends on the token it's in. The expression $(command) is a modern synonym for `command` which stands for command substitution; it means run command and put its output here. So

echo "Today is $(date). A fine day."

will run the date command and include its output in the argument to echo. The parentheses are unrelated to the syntax for running a command in a subshell, although they have something in common (the command substitution also runs in a separate subshell).

By contrast, ${variable} is just a disambiguation mechanism, so you can say ${var}text when you mean the contents of the variable var, followed by text (as opposed to $vartext which means the contents of the variable vartext).

The while loop expects a single argument which should evaluate to true or false (or actually multiple, where the last one's truth value is examined -- thanks Jonathan Leffler for pointing this out); when it's false, the loop is no longer executed. The for loop iterates over a list of items and binds each to a loop variable in turn; the syntax you refer to is one (rather generalized) way to express a loop over a range of arithmetic values.

A for loop like that can be rephrased as a while loop. The expression

for ((init; check; step)); do
    body
done

is equivalent to

init
while check; do
    body
    step
done

It makes sense to keep all the loop control in one place for legibility; but as you can see when it's expressed like this, the for loop does quite a bit more than the while loop.

Of course, this syntax is Bash-specific; classic Bourne shell only has

for variable in token1 token2 ...; do

---

(Somewhat more elegantly, you could avoid the echo in the first example as long as you are sure that your argument string doesn't contain any % format codes:

date +'Today is %c. A fine day.'

Avoiding a process where you can is an important consideration, even though it doesn't make a lot of difference in this isolated example.)

$() means: "first evaluate this, and then evaluate the rest of the line".

Ex :

    echo $(pwd)/myFile.txt

will be interpreted as

    echo /my/path/myFile.txt

On the other hand ${} expands a variable.

Ex:

    MY_VAR=toto
    echo ${MY_VAR}/myFile.txt

will be interpreted as

    echo toto/myFile.txt

2. > Why can't I use it as bash$ while ((i=0;i<10;i++)); do echo $i; done

I'm afraid the answer is just that the bash syntax for while just isn't the same as the syntax for for.

1. your understanding is right. For detailed info on {} see bash ref - parameter expansion

2. 'for' and 'while' have different syntax and offer different styles of programmer control for an iteration. Most non-asm languages offer a similar syntax.

With while, you would probably write i=0; while [ $i -lt 10 ]; do echo $i; i=$(( i + 1 )); done in essence manage everything about the iteration yourself