There is a possible difference, but it is not clear what the outcome would be in case you got sued. The technical fact is that playing and transmitting sound by computer involves copying. 17 USC 106 says
Subject to sections 107 through 122, the owner of copyright under this
title has the exclusive rights to do and to authorize any of the
following: (1) to reproduce the copyrighted work in copies or
phonorecords
and copies are defined as
material objects, other than phonorecords, in which a work is fixed by
any method now known or later developed, and from which the work can
be perceived, reproduced, or otherwise communicated, either directly
or with the aid of a machine or device. The term “copies” includes the
material object, other than a phonorecord, in which the work is first
fixed.
The courts have not ruled definitively on what a "material object" is, but there is a good chance that sound transmitted by computer becomes a disk file (in a supposedly temporary buffer). In the case MAI Systems Corp. v. Peak Computer, the court found that a computer makes a copy of a program when it reads from hard disk into RAM so that the program can be executed, and is thus a copy under Title 17. The computer-owner was licensed to make such copies, but the repair company (defendant) was not a licensee. The case largely centered around the question of what a copy is, and the court concluded that
the loading of copyrighted computer software from a storage medium
(hard disk, floppy disk, or read only memory) into the memory of a
central processing unit ("CPU") causes a copy to be made. In the
absence of ownership of the copyright or express permission by
license, such acts constitute copyright infringement.
Even though RAM is somewhat volatile, it is
sufficiently permanent or stable to permit it to be perceived,
reproduced, or otherwise communicated for a period of more than
transitory duration.
17 USC 117 has some exceptions to the copyright holder's rights regarding programs (not data) and repairs, neither of which would deny protection to background music (plus: the statute is framed in terms of actual owners of software, not licensees). There are also performance exceptions in 17 USC 110, mostly limited to educational or religious performances. But this is where there could exist an exception. (4) enumerates an exceptional case that is not infringement:
performance of a nondramatic literary or musical work otherwise than
in a transmission to the public, without any purpose of direct or
indirect commercial advantage and without payment of any fee or other
compensation for the performance to any of its performers, promoters,
or organizers, if—
Your plan is not a transmission to the public, and I assume there is no money involved. The two "if" clauses are about money, and I suppose there is no money involved in this party.
The problem is that this exceptional section is about performances and not making copies (this is a separate right protected under 17 USC 106). No exception has been created for the kind of copying that would result by computer-transmitting copies of protected works.
So yes, there is a difference: when you are together in a room, you can "perform" the work. That doesn't mean that there is a real danger of an infringement lawsuit, and it is possible that you have permission from the licensor to make such internet-transmitted "copies".
