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
Yes
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. (PHB)
As long as both the weapon you touch and the pact weapon you conjure are light weapons (or you have the Dual Wielder feat), you make make a bonus action when you take an attack action to attack with both weapons.
Hex Warrior states:
you can touch one weapon that you are proficient with and that lacks
the two-handed property...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. (XGtE)
So, the only restrictions from Hex Warrier are that the weapon cannot be two handed and you must be proficient.
Pact of the Blade states:
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 (see chapter 5 for weapon options). (PHB)
There actually isn't really any weapon restrictions with the Pact of the Blade feature.
So, as long as you use a light weapon for these features (or have the Dual Wielder feat) you can attack with both, one in your primary hand as an action and the other in your off hand as a bonus action.
To allay the concerns you expressed in the first draft of your question, yes, Warlocks do get bonus actions under the same conditions as everybody else:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. (PHB)
Since you are using the Two-Weapon Fighting feature of the game, as long as you meet the conditions therein, you are able to take a bonus action.
You do only get one bonus action per turn no matter what, so you cannot attack with both weapons if you've already used that on your turn. But otherwise, Yes you can easily use a bonus action to attack with the weapon you touch and the pact weapon you conjure.
Best Answer
Yes
In D&D 5e, a rule means what it says and no more (unless the DM rules otherwise, which they are always entitled to do). Per the Hex Warrior description in the question:
A lance lacks the two-handed property, and qualifies for this requirement, even though you must wield it in two hands when not mounted.
Jeremy Crawford has ruled similarly in the related situation of the monk wielding a quarterstaff in two hands, despite weapons with the two-handed property being prohibited from the category of monk weapons:
Crawford is clear here in his intent: wielding a weapon with the two-handed property and wielding a weapon in two hands are not functionally equivalent in the rules.
The DM, of course, is always free to rule otherwise, particularly in situations like this where it may make sense to do so.