Yes, they can be two separate weapons

Based on your question, I'm assuming you are pulling your Hexblade class out of Unearthed Arcana, instead of Xanathar's Guide.

XGTE adds this clarification:

If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type.

This raised a further question in someone (same question as yours, actually), which was volleyed up to Jeremy Crawford (Official Voice of Rulings for WotC)

Q: So Hex Warrior, the way it is worded has perked up a question for me. Can you have both a bonded regular/magic weapon and a pact weapon gaining the Cha bonus benefit at the same time?

A: The Hex Warrior feature is intentionally worded to extend its benefit to two potential weapons: the weapon you touch and a pact weapon you conjure.

https://twitter.com/JeremyECrawford/status/930235396792786944

The way it is written in UA, NO.

Note the use of is, instead of something like gains a +2 bonus

Any weapon you create using your Pact of the Blade feature is a +2 weapon. This invocation doesn’t affect a magic weapon you transformed into your pact weapon.

This is similar to the writing in Armors, in which your AC is something, and stacking armors (somehow) wouldn't stack bonuses.

The way it is written in XGtE, probably NO.

For the XGtE,

In addition, the weapon gains a +1 bonus to its attack and damage rolls

which would stack with another effect that said something on the lines of

In addition, the weapon gains a +2 bonus to its attack and damage rolls

except that it is explicitly states

unless it is a magic weapon that already has a bonus to those rolls.

and Pact Blade counts as a magical weapon (at least for resistances against non-magic weapons), as stated

You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it. You are proficient with it while you wield it. This weapon counts as magical for the purpose of overcoming Resistance and immunity to nonmagical attacks and damage.

While not explicitly stated that it counts as a magical weapon for the purpose of the bonus, it seems it is intended to not stack.

_{Note that the UA usually is not balanced (the point of it is to playtest and balance) and you should take care with using this content. From my experience, the writting was also not refined by then, as can be seen in the difference between the actual release and the UA version. You could suppose the intended purpose of what was written on UA is what is written on the official release, but that would not be RAW.}