В чем разница употребления particularly и specially?

Particularly [= especially]: Особенно

The restaurant is particularly popular with young people.
We are hoping to expand our business, particularly in Europe.

- not particularly
a) not very: не очень (not very much)
I'm not particularly impressed with their performance.
'Do you want to come to the party?' 'Not particularly.'

• The cake was especially good.
• This part is especially interesting.
• Everyone loved it, especially the children.
• You should call first, especially if you're going to be late.
"Particilarly" (Especially) never comes at the start of a sentence - никогда не применяется в начале предложения
• He loves fruit. He especially likes kiwis (NOT Especially he likes ...).

Use "Specially" to say that something is done or made for a particular purpose - Специально

• I got this specially for you.
• specially designed equipment