All IP's are "static" in the web hosting world. The term static versus dynamic (i.e. it changes) doesn't apply here. It is only a term for dialup / isp.
The relevant terms are Shared IP and Dedicated IP.
Shared IP is when one IP Address is used by many web sites. This is made possible by the HTTP 1.1 standard which all browsers support.
Back in the dark age, when some browsers only know HTTP 1.0, they won't work with shared ip. But that age is long gone now.
Dedicated IP is when one ip address is dedicated to only one website. This is still needed these days if you want to install an SSL certificate, because the SSL protocol / encryption happens before the exchange of the HTTP header and the server doesn't know yet what site the browser is requesting, so it won't be able to present the correct certificate if it is a shared ip.
There have been myths about search engines not liking shared ip sites. This myth might have been true in the dark ages, but it is certainly not true now.