Difference between Tacit Contracts and Implied Contracts:

Dictionary meaning of 'tacit' is: Implied by or inferred from actions or statements; so both are same. 

If we really try to dig dipper then 'tacit' also could mean something which is not spoken but understood from non-verbal communication. Non-verbal communication includes, winking, sighs, tone and pitch and silence. 

Eg: She indicated her tacit approval by smiling and winking.

In this extended sense, sometimes an implied contract could involve express verbal communication, however no such express communication is required in most cases of a tacit contract. 

in the above, the verbal communication, which is refereed to, is not happening between the offerer and offeree; but is happening between one of these and a third party:

For example: 
while The conductor of a bus is telling X- a general inquirer- that the fare is Rs 10 to Railway station, Y- an intending passenger- hears this and  boards the bus to the same destination. Here though there is no direct offer by the conductor to this particular passenger yet from what he overheard he can take that as an implied offer and when he boards the bus there is an implied acceptance from him. So this would be a case of an implied contract.

As we do not see any subtlety in boarding a bus we may not classify this as a tacit contract. 

To avoid misunderstanding:
As per section 9 of Indian Contract Act- 1872: 

Promises, express and implied are defined as following:
In so far as the proposal or acceptance of any promise is made in words, the promise is said to be express. In so far as such proposal or acceptance is made otherwise than in words, the promise is said to be implied.

So, where the offer or acceptance is not made in words- written or verbal- it is a case of implied promise. By extension, existence of an implied promise would give rise to an implied contract. 

Now if we consider Implied contracts to be a set then tacit contracts would be a subset within this set. So essentially tacit contracts would also be implied contracts. 

The subtlety in the offer or the acceptance would make it a tacit contract.

The word 'Tacit' finds no mention anywhere in the Act (Indian Contract Act- 1872).

Here's an objective example of the importance of appropriate drafting of contracts:

Dr Das is a reputed consultant who facilitates Hospitals getting NABH- National Accreditation Board for Hospitals- certificates, which helps them optimize their revenue. As this indicates quality now government hospitals are also interested to get these certifications.

While accepting such assignments Dr Das gets a standardized agreement signed. Here’s one of the clauses of such an agreement.

"The contract is valid for a year or till the certificate is received (whichever is earlier)."

Missing out the clause in the parentheses (brackets), while accepting a contract from the state government cost very heavily to Dr XYZ Das.

The state government people were innocent of any firm timeline. But due to the open-endedness of the contractual terms Dr Das was bound to provide them services, while the inordinate delays were entirely attributable to the inefficiency and gross callousness of Government officials, for ages and the fees was fixed.

(This Draft would be further populated with similar real life examples to be of benefit to professionals practicing the trade of Drafting etc.)