If you have $1M in a Swiss bank account earning capital gains, and don't declare it to the IRS - that's 'tax evasion'.
If you have a company in Switzerland generating revenue, and decide not to bring back your profits to America to get hit with another tax, and just let it sit in Switzlerland - that's a 'tax avoidance' strategy.
'Tax evasion' = illegal.
'Tax avoidance' = doing everything you can within the boundaries of the law to not pay taxes. There are some wierd loopholes due to the way taxation works across borders.
Where it gets prickly is when companies game the system and find ways to reduce tax that the sovereign clearly would outlaw, but cannot for structural or political reasons. Still not illegal, but not exactly awesome either.
Tax avoidance does not. It involves complete honesty with the tax authorities, who then charge you less tax, as the rules state they should. The definition of "avoidance" is therefore intensely political - avoidance tends to be defined as lawful behaviour by other people the speaker would prefer paying for government instead of them!