Differences between single quotes and double quotes in shell programming

The following uses a simple Shell Program Note.

Debian :~ /Learn/shell # Cat phonebook
Alice chebba 973-555-2015
Barbara Swingle 201-555-9257
Liz stachiw 212-555-2298
Susan Goldberg 201-555-7776
Susan topple 212-555-4932
Tony iannino 973-555-1295
Stromboli pizza 973-555-9478
Debian :~ /Learn/shell #

Debian :~ /Learn/shell # Cat Lu
# Look someone up in the phone book
Grep "$1" Phonebook
Debian :~ /Learn/shell #

This is the correct Lu program. The following shows the running result.

Debian :~ /Learn/shell #./Lu 'Susan t'
Susan topple 212-555-4932
Debian :~ /Learn/shell #./Lu Tony
Tony iannino 973-555-1295
Debian :~ /Learn/shell #

If Lu is written as ① grep $1 phonebook or ② grep '$ 1' phonebook, the following error will occur (Why ?).

Result 1:

Debian :~ /Learn/shell #./Lu Tony // The result is correct.
Tony iannino 973-555-1295
Debian :~ /Learn/shell #./Lu 'Susan t' // The result is incorrect.
Grep: T: no such file or directory
Phonebook: Susan Goldberg 201-555-7776
Phonebook: Susan topple 212-555-4932
Debian :~ /Learn/shell #

② Results:

Debian :~ /Learn/shell #./Lu Tony // The result is incorrect.
Debian :~ /Learn/shell #./Lu 'Susan t' // The result is also incorrect.
Debian :~ /Learn/shell #