*ahem*
A Tribute Summon is any Normal Summon that involves Tributing 1 or more monsters (very usually Level 5 or higher monsters). All Tribute Summons are Normal Summons, but not all Normal Summons are Tribute Summons.
Consider Level Conversion Lab. If you make your B.E.S. Crystal Core a Level 3 monster, you can Normal Summon it without Tribute. This means it's NOT a Tribute Summon, but it still IS a Normal Summon. Since B.E.S. Crystal Core gains its Core Counters when it is Normal Summoned, it will STILL get its Core Counters even in this case.
The opposing example is Mobius the Frost Monarch. He needs to be Tribute Summoned in order to get his effect. If Level Conversion Lab has made him Level 3, you can certainly Normal Summon him, but you WON'T get his effect (because he wasn't Tribute Summoned).
~ ~ ~ ~ ~ ~ ~ ~ ~
B.E.S. Covered Core
Effect Monster (Machine / EARTH / 7 Stars / ATK 2500 / DEF 800)
When this card is Normal Summoned, put 2 counters on it. This card cannot be destroyed by battle. If this card attacks or is attacked, at the end of the Damage Step toss a coin and call it. If you call it wrong, remove 1 counter. If this card battles without a counter, destroy it at the end of the Damage Step.