Is there any difference in terms of MEANING between "to infinitive and the infinitive without to"?

For example : To have Vs have.
In this decotextualized comparison if some one asks you to tell the difference in meaning between these two. What would you say?

Do they have the same meaning? I think they must be similar and the only difference is their usage in sentences. Sometimes we should use one over the other with certain verbs.

Question

Is there any difference in terms of MEANING between "to infinitive and the infinitive without to"?

For example : To have Vs have. 
In this decotextualized comparison if some one asks you to tell the difference in meaning between these two.  What would you say?

Do they have the same meaning? I think they must be similar and the only difference is their usage in sentences. Sometimes we should use one over the other with certain verbs.

Answer

I agree with you. They differ in terms of usage in the sentence. For instance, an infinitive without to follows modal verbs while some specific verbs must be followed by to infinitive.

e.g:
You can have some tea.
I'd like to have some coffee.

Answer

First off, the infinitive has no meaning aside from naming the action expressed by the verb. But it's unique in that it never refers to any specific person (=doesn't conjugate for person or tense), and can act like a noun: "To complain about the president would be considered treason in some countries."

The only difference is in syntax: some grammatical forms require *to*: "I want/need/try *to* help." Other forms don't take it at all, like modal verbs: "I can, will, should –[to] go." And with some forms, it's optional: "This book will help (to) teach you English."

Answer

By the way, the infinitive without *to* is called the plain infinitive.