Both are entirely separate, but tier (e.g. Tour Master) may be related to both of them nowadays.
A) Levels describe certains steps of experience gained, that is industry. You have to amass experience points - XPs. A "Reference Table Level vs. XPs" here shows the development (quite exponential!)
B) "Average" comes from the scores of ranked strokeplay rounds. It resets at each tier and is non-linear once it really counts - look up "saturation".
C) Tier promotion:
Traditionally, a certain average in a certain tier, combined with a certain minimum no. of rounds, grants promotion - there are tables available.
On modile devices, the lower tiers are also dependant on Levels, because the typical mobile games are all practice rounds.
jiggsie:How can a player have a 53 average, be level 105 and still be a tour master
L105 means that he amassed a lot of XPs by playing much and/or a long time.
53 average means that he has scored extraordinarily well in (a few) ranked strokeplay rounds, probably as a TM, but not yet 50 rounds which would propel him to the Legend tier.
Apparently, this player has playing habits that differ largely from the average player. That's a loose indication but far from a proof that he might deviate from the rules.