Main Difference
The main difference between Percentage and Average is that the Percentage is a Number or ratio as a fraction of 100 and Average is a colloquial term for the central tendency (middle or typical number of a list of numbers, including mean, median and mode)

Percentage
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, “%”, or the abbreviations “pct.”, “pct”; sometimes the abbreviation “pc” is also used. A percentage is a dimensionless number (pure number).

Average
In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often “average” refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.

Percentage (noun)
The amount, number or rate of something, regarded as part of a total of 100; a part of a whole.
“A high percentage of secondary school leavers take a gap year.”

Percentage (noun)
A share of the sales, profits, gross margin or similar.
“She gets a percentage for every vacuum cleaner sold.”

Percentage (noun)
Benefit or advantage.
“There was no percentage in staying at home.”

Average (noun)
The arithmetic mean.
“The average of 10, 20 and 24 is (10 + 20 + 24)/3 = 18.”

Average (noun)
Any measure of central tendency, especially any mean, the median, or the mode. from c. 1735

Average (noun)
Financial loss due to damage to transported goods; compensation for damage or loss. from 15th c.

Average (noun)
Customs duty or similar charge payable on transported goods.

Average (noun)
Proportional or equitable distribution of financial expense.

Average (noun)
An scoring record, etc.
“batting average”

Average (noun)
In the corn trade, the medial price of the several kinds of grain in the principal corn markets.

Average (noun)
The service that a tenant owed his lord, to be done by the animals of the tenant, such as the transportation of wheat, turf, etc.

Average (adjective)
Constituting or relating to the average.
“The average age of the participants was 18.5.”

Average (adjective)
Neither very good nor very bad; rated somewhere in the middle of all others in the same category.
“I soon found I was only an average chess player.”

Average (adjective)
Typical.
“The average family will not need the more expensive features of this product.”

Average (adjective)
Not outstanding, not good, banal; bad or poor.

Average (verb)
To compute the average of, especially the arithmetic mean.
“If you average 10, 20 and 24, you get 18.”

Average (verb)
Over a period of time or across members of a population, to have or generate a mean value of.
“The daily high temperature last month averaged 15°C.”
“I averaged 75% in my examinations this year.”

Average (verb)
To divide among a number, according to a given proportion.
“to average a loss”

Average (verb)
To be, generally or on average.

Percentage (noun)
a rate, number, or amount in each hundred
“a large percentage increase”
“the percentage of Caesareans at the hospital was three per cent higher than the national average”

Percentage (noun)
any proportion or share in relation to a whole
“only a tiny percentage of the day trippers are aware of the village’s gastronomic distinction”

Percentage (noun)
an amount, such as an allowance or commission, that is a proportion of a larger sum of money
“I hope to be on a percentage”

Percentage (noun)
personal benefit or advantage
“I don’t see the percentage in selling perfectly good furniture”

Average (noun)
a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number
“the proportion of over60s is above the EU average of 19 per cent”

Average (noun)
an amount, standard, level, or rate regarded as usual or ordinary
“underground water reserves are below average”
“they take about thirty minutes on average”

Average (noun)
the apportionment of financial liability resulting from loss of or damage to a ship or its cargo.

Average (noun)
reduction in the amount payable under an insurance policy, e.g. in respect of partial loss.

Average (adjective)
constituting the result obtained by adding together several amounts and then dividing this total by the number of amounts
“the average temperature in May was 4°C below normal”

Average (adjective)
of the usual or ordinary amount, standard, level, or rate
“a woman of average height”

Average (adjective)
having qualities that are seen as typical of a particular person, group, or thing
“the average lad likes a good night out”

Average (adjective)
mediocre; not very good
“a very average director making very average movies”

Average (verb)
amount to or achieve as an average rate or amount over a period of time; mean
“annual inflation averaged 2.4 per cent”

Average (verb)
calculate or estimate the average of
“they earned only £35 weekly when their seasonal earnings were averaged out”

Average (verb)
result in an even distribution; even out
“it is reasonable to hope that the results will average out”

Average (verb)
result in an average figure of
“the cost should average out at about £6 per page”