Distribution has to do with the availability of books.  POD books are distributed through Ingram and Baker and Taylor when the publisher prints through the Ingram print division (Lightning Source aka LSI).  If the publisher is actually a printer, he may not use LSI and in that case he will not be able to offer distribution through Ingram. Most POD publishers do offer this distribution, but there are some who charge extra for it.

Does it matter if you have Ingram distribution?  I think it does.  Without it, making your book available is going to be ever more difficult.  It won't be listed on Amazon or with other booksellers unless you make those arrangements yourself. Potential readers won't be able to go into a bookstore and have the clerk find your book on their system.

Without distribution, your book is invisible.  No one will be able to find it.

Marketing, on the other hand, has to do with making people want to find the book. It's out there; it's available on the distribution systems, but who cares?  So are over a million other books.  Why would anyone look for yours?  That's what marketing is all about.

Marketing includes everything from sending out postcards to getting the book reviewed to getting out and doing book signings or seminars.  Most publishers will put up a web page for your book and you'll be able to market through the web as well. You might also want to put up your own domain name web site.  It's like that old question that advertisers ask: "Do you know what happens when you don't advertise?"  Answer: "Nothing."

Advertising is when you pay for placement in the media whereas publicity is when you don't pay for it (at least not directly to the media).  The key to your marketing strategy is going to therefore be a press release because that's what you send out to get free publicity.