With email marketing, you send newsletter to your list of subscribers. On the opposite, with cold email you send emails to strangers in order to get clients, backlinks or network.
Cold email is suited for outbound. This means than your objective is to turn 'cold' prospects who don't know about your product/service into leads, before eventually turning them into paying customers. We also talk about 'warm' leads when you cold email a prospect that might have interacted with your content before.
Email marketing is suited for inbound. This means than your objective is to turn 'warm' leads who signed up to your product or service into paying customers. Email marketing is also use to send newsletters to a list without any intent of selling anything.
With cold emails, you have less chances to fall into spam because you use your own SMTP server from you email provider. With email marketing, you share your SMTP server with other people. If one of these people is spammy with his/her emails, it will affect your own deliverability. To prevent that, email marketing software offers you the possibility to set up your own smtp server for higher costs.
In any way, don't use an email marketing software to send cold emails. You will have spam issues, it's not recommended and these softwares have not been designed for this use.
Yes, you can use a cold email software like Breakcold for you cold email outreach and an email marketing software like SendGrind for your email marketing.
At Breakcold, we're fan of the work done at Sendgrid, Flodesk but we personally use Customer.io for precision.
Shameless plug here, we do recommend our own software Breakcold :)