mail deleted from iPhone does not delete from laptop?

Email account is POP

POP accounts do not make Reading Mail from multiple devices easy or efficient. The POP model says there is exactly ONE Reading device, and and the Server relies on that Reading device to manage everything locally (i.e., on your Mac) the way it wants. For example, an Email that is Read will be marked "already Read" locally in your email Reader, but NOT on the Server. If you use a Browser to look at the Server, those messages will not say "already Read'.

When you log in to a POP Server with another device like an iPhone, you see the "Raw" information that is still on the Server, not cleaned up by the settings made locally by the original Mail Reading device (on your Mac).

IMAP changes this model so the Server does a little more of the work. IMAP allows update of Server information by multiple Reading devices, so it marks messages that were read on any device as "already Read", and emails discarded on any device as discarded. It also allows an option to store Sent messages on the Server (so they can be referenced by either device), rather than having one group on your Mac and another on your Phone, and no easy way to refer to both.

Some email providers, such as EarthLink, have bowed to pressure from Users and added IMAP support option on the same accounts.

Others, such a Verizon, have said, "No, we do not offer that." which really means, "That would cost us money, so it must be YOUR problem."