The gemara says that when one loses track of when shabbos is, they should count six days and keep the seventh as Shabbos. The gemara makes it clear that the purpose is not because we assume that the 7th day will actually be shabbos, but rather we don't want him to forget the concept of shabbos (rashi) therefore the Rabbonon impose this system to remember the concept of Shabbos. The gemara also says that it is forbidden to do melacha any of the days of the week, beyond what is needed to survive for that day, because every day is a safeik shabbos and is permitted only for pikuach nefesh. The M.B. says that we aren't entitled to go after the "rov", the majority of days which aren't shabbos because one of the seven is definitely shabbos and therefore it qualifies as kavuah where we don't follow the majority.
The gemara has trouble figuring out what makes the 7th day stand out over the rest since on all days he can do what is needed to survive but not more. The only thing that the gemara comes up with is that on the 7th day he will make kiddush as it comes in and havdala as it goes out - that is the only difference between his 7th day and all other days. Tosafos asks why doesn't the gemara say that he can travel beyond his techum all other days but not on the 7th day? Tosafos offers two answers: 1. It is not a significant difference between the 7th day and the 6 earlier days by passively sitting and not travelling. 2. He can travel even on the 7th day since that is necessary to get him out of his present situation. Regarding the second answer of Tosafos, there seems to be a machlokes Ran and Ritva as to whether we allow him to travel beyond his techum, even according to R. Akiva where techum is d'oraysa, or are we only permissive because it is considered d'rabonon.
According to the second answer of Tosafos that a passive recognition is sufficient, the Biur Halacha questions why we don't say that Shabbos stands out in that he wears tefillin everyday except his 7th day. From this the Biur Halacha concludes that Tosafos must hold that he actually would need to put on tefillin everyday including his 7th day.
It comes out that on a Torah level, we regard every day as shabbos and don't allow any work beyond pikuach nefesh, but on the other hand regard every day as not being shabbos and require him to put on tefillin.