i really don;t understand why the connection type should matter unless when not on WiFi it goes through different path.
The reason it matters is anti-spam filtering.
SMTP e-mail was designed as an insecure system.
We've been living with the consequences of that for years.
So ISPs provide an outgoing SMTP server, for the use of *their* clients.
To prevent it being abused by others, it may be configured to only allow outbound mail from *their* IP address-block, ie their customers on-network.
To allow their customers to continue to send via their outbound SMTP when the customer is off-network, SMTP authentication has been devised.
So in general, most ISPs won't allow outbound SMTP via their servers if you are coming in from an IP address which is external to them. They may allow a work-around with authentication.
ETA: And as Kim said, even when you're off-network, and your SMTP server is allowing external authenticated access, it's possible the 'external ISP' you are temporarily connecting via does not allow standard SMTP sessions out of it's network, forcing users to use the 'temporary connection ISP' SMTP relays. Work-arounds involve your SMTP host accepting connections on an alternate port. It's all a bit ugly.