Yes, all of these systems of magic are linked (see: http://coppermind.net/wiki/Cosmere), all forms of magic in the cosmere are linked through the 3 planes/realms:
You can read up on these different aspects by looking up the cosmere's Realmatic Theory
It's theorised that the over arching magic systems will end up on some kind of table that describes how the systems mesh with one another (something like the allomantic table of push/pull & external/internal).
We know that all magic in the cosmere is a form of Investiture, which exists in all three of the afore mentioned realms. Investiture also obeys it's own version of thermodynamics, by which I mean it cannot be created or detroyed. Only moved from one place to another eg. Biochromatic breath.
Another big part of the collective magic system is Intent. Each shard has intent, and that intent shapes the world's unique magic system (this implies that some magics are not entirely based on each shard, but possibly something else.. (Q160)) eg. Ruin (of the Mistborn series) had destructive intent, which is easily visible in something like the Koloss, his creation. To breed, they would kill 4 humans and then implant spikes used to kill these people into another person (it uses Hemalurgy if I'm not mistaken). This is a very destructive process, you put in 5 people and get 1 Koloss. They're strong, but not an awful lot else.
There is also intent in using Investiture (magic of any kind), for instance in Warbreaker we know that you must issue commands that fit your will specifically, or the command will not work as planned. Another form of Investiture is in Feruchemy, you invest in your metalminds.
Next up is the focus of each magical system, we know that there are multiple unique systems to some shards.
Sel magic systems (Elantris & The Emperors Soul)
Scadrial magic systems (Mistborn)
Roshar magic systems (Stormlight Archives)
Nalthis magic systems (Warbreaker)
We know that some of these systems do not work well together (Q143), however we know that some are "universal" eg. 'Hemalurgy can be used to bestow any form of magic]5(Q143 again) however it's noted by Hoid when he world hops for what we think is the first time, that "it's different here" or something like that (again I will find a reference after work).. I'm afraid only Brandon Sanderson himself knows all the links at this point.
It's also worth noting that there are "magical sciences" (defined as the use of Investiture without alteration of the Spiritweb) eg. Fabrials from Roshar (Stormlight Archives), different coloured gems, capture spren and require some mechanical configuration to cause an effect (sounds like something similar to Biochromatic breath?), we can also see here all the components needed for magic: Physical - Mechanical setup, Spiritual - Biochromatic breath (or maybe better to call it, the "magic") and Cognitive - the Spren.